[{"main_file_link":[{"url":"https://d-nb.info/1139356542/34","open_access":"1"}],"year":"2017","type":"dissertation","citation":{"ieee":"S. Peitz, Exploiting structure in multiobjective optimization and optimal control. 2017.","short":"S. Peitz, Exploiting Structure in Multiobjective Optimization and Optimal Control, 2017.","bibtex":"@book{Peitz_2017, title={ Exploiting structure in multiobjective optimization and optimal control}, DOI={10.17619/UNIPB/1-176}, author={Peitz, Sebastian}, year={2017} }","mla":"Peitz, Sebastian. Exploiting Structure in Multiobjective Optimization and Optimal Control. 2017, doi:10.17619/UNIPB/1-176.","chicago":"Peitz, Sebastian. Exploiting Structure in Multiobjective Optimization and Optimal Control, 2017. https://doi.org/10.17619/UNIPB/1-176.","apa":"Peitz, S. (2017). Exploiting structure in multiobjective optimization and optimal control. https://doi.org/10.17619/UNIPB/1-176","ama":"Peitz S. Exploiting Structure in Multiobjective Optimization and Optimal Control.; 2017. doi:10.17619/UNIPB/1-176"},"_id":"10594","file":[{"file_size":16636801,"file_id":"16298","creator":"speitz","date_updated":"2020-03-13T12:52:50Z","content_type":"application/pdf","success":1,"relation":"main_file","file_name":"Dissertation_Peitz.pdf","date_created":"2020-03-13T12:52:50Z","access_level":"closed"}],"author":[{"first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","last_name":"Peitz","id":"47427"}],"file_date_updated":"2020-03-13T12:52:50Z","has_accepted_license":"1","status":"public","date_created":"2019-07-10T08:12:22Z","abstract":[{"lang":"eng","text":"Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute\r\nthe set of optimal compromises (the Pareto set) between the conflicting objectives.\r\n\r\nSince – in contrast to the solution of a single objective optimization problem – the\r\nPareto set generally consists of an infinite number of solutions, the computational\r\neffort can quickly become challenging. This is even more the case when many problems have to be solved, when the number of objectives is high, or when the objectives\r\nare costly to evaluate. Consequently, this thesis is devoted to the identification and\r\nexploitation of structure both in the Pareto set and the dynamics of the underlying\r\nmodel as well as to the development of efficient algorithms for solving problems with\r\nadditional parameters, with a high number of objectives or with PDE-constraints.\r\nThese three challenges are addressed in three respective parts.\r\n\r\nIn the first part, predictor-corrector methods are extended to entire Pareto sets.\r\nWhen certain smoothness assumptions are satisfied, then the set of parameter dependent Pareto sets possesses additional structure, i.e. it is a manifold. The tangent\r\nspace can be approximated numerically which yields a direction for the predictor\r\nstep. In the corrector step, the predicted set converges to the Pareto set at a new\r\nparameter value. The resulting algorithm is applied to an example from autonomous\r\ndriving.\r\n\r\nIn the second part, the hierarchical structure of Pareto sets is investigated. When\r\nconsidering a subset of the objectives, the resulting solution is a subset of the Pareto\r\nset of the original problem. Under additional smoothness assumptions, the respective subsets are located on the boundary of the Pareto set of the full problem. This\r\nway, the “skeleton” of a Pareto set can be computed and due to the exponential\r\nincrease in computing time with the number of objectives, the computations of\r\nthese subsets are significantly faster which is demonstrated using an example from\r\nindustrial laundries.\r\n\r\nIn the third part, PDE-constrained multiobjective optimal control problems are\r\naddressed by reduced order modeling methods. Reduced order models exploit the\r\nstructure in the system dynamics, for example by describing the dynamics of only the\r\nmost energetic modes. The model reduction introduces an error in both the function values and their gradients, which has to be taken into account in the development of\r\nalgorithms. Both scalarization and set-oriented approaches are coupled with reduced\r\norder modeling. Convergence results are presented and the numerical benefit is\r\ninvestigated. The algorithms are applied to semi-linear heat flow problems as well\r\nas to the Navier-Stokes equations.\r\n"}],"user_id":"47427","ddc":["510"],"language":[{"iso":"eng"}],"date_updated":"2022-01-06T06:50:46Z","oa":"1","doi":"10.17619/UNIPB/1-176","department":[{"_id":"101"}],"project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"publication_status":"published","title":" \tExploiting structure in multiobjective optimization and optimal control"},{"date_updated":"2022-01-06T06:52:51Z","_id":"16499","doi":"10.1007/s00205-009-0240-y","year":"2009","type":"journal_article","citation":{"mla":"Biasco, Luca, and Laura Di Gregorio. “A Birkhoff–Lewis Type Theorem for the Nonlinear Wave Equation.” Archive for Rational Mechanics and Analysis, 2009, pp. 303–62, doi:10.1007/s00205-009-0240-y.","bibtex":"@article{Biasco_Di Gregorio_2009, title={A Birkhoff–Lewis Type Theorem for the Nonlinear Wave Equation}, DOI={10.1007/s00205-009-0240-y}, journal={Archive for Rational Mechanics and Analysis}, author={Biasco, Luca and Di Gregorio, Laura}, year={2009}, pages={303–362} }","apa":"Biasco, L., & Di Gregorio, L. (2009). A Birkhoff–Lewis Type Theorem for the Nonlinear Wave Equation. Archive for Rational Mechanics and Analysis, 303–362. https://doi.org/10.1007/s00205-009-0240-y","ama":"Biasco L, Di Gregorio L. A Birkhoff–Lewis Type Theorem for the Nonlinear Wave Equation. Archive for Rational Mechanics and Analysis. 2009:303-362. doi:10.1007/s00205-009-0240-y","chicago":"Biasco, Luca, and Laura Di Gregorio. “A Birkhoff–Lewis Type Theorem for the Nonlinear Wave Equation.” Archive for Rational Mechanics and Analysis, 2009, 303–62. https://doi.org/10.1007/s00205-009-0240-y.","ieee":"L. Biasco and L. Di Gregorio, “A Birkhoff–Lewis Type Theorem for the Nonlinear Wave Equation,” Archive for Rational Mechanics and Analysis, pp. 303–362, 2009.","short":"L. Biasco, L. Di Gregorio, Archive for Rational Mechanics and Analysis (2009) 303–362."},"page":"303-362","language":[{"iso":"eng"}],"title":"A Birkhoff–Lewis Type Theorem for the Nonlinear Wave Equation","user_id":"47427","author":[{"first_name":"Luca","full_name":"Biasco, Luca","last_name":"Biasco"},{"last_name":"Di Gregorio","full_name":"Di Gregorio, Laura","first_name":"Laura"}],"department":[{"_id":"101"}],"publication":"Archive for Rational Mechanics and Analysis","publication_status":"published","publication_identifier":{"issn":["0003-9527","1432-0673"]},"status":"public","date_created":"2020-04-14T09:59:20Z"},{"doi":"10.1016/j.protcy.2016.08.059","_id":"8758","intvolume":" 26","date_updated":"2022-01-21T14:10:10Z","language":[{"iso":"eng"}],"type":"conference","citation":{"short":"J. Eckstein, S. Peitz, K. Schäfer, P. Friedel, U. Köhler, M. Hessel von Molo, S. Ober-Blöbaum, M. Dellnitz, in: Procedia Technology, 3rd International Conference on System-Integrated Intelligence: New Challenges for Product and Production Engineering, 2016, pp. 465–472.","ieee":"J. Eckstein et al., “A comparison of two predictive approaches to control the longitudinal dynamics of electric vehicles,” in Procedia Technology, 3rd International Conference on System-Integrated Intelligence: New Challenges for Product and Production Engineering, 2016, vol. 26, pp. 465–472, doi: 10.1016/j.protcy.2016.08.059.","chicago":"Eckstein, Julian, Sebastian Peitz, Kai Schäfer, Patrick Friedel, Ulrich Köhler, Mirko Hessel von Molo, Sina Ober-Blöbaum, and Michael Dellnitz. “A Comparison of Two Predictive Approaches to Control the Longitudinal Dynamics of Electric Vehicles.” In Procedia Technology, 3rd International Conference on System-Integrated Intelligence: New Challenges for Product and Production Engineering, 26:465–72, 2016. https://doi.org/10.1016/j.protcy.2016.08.059.","ama":"Eckstein J, Peitz S, Schäfer K, et al. A comparison of two predictive approaches to control the longitudinal dynamics of electric vehicles. In: Procedia Technology, 3rd International Conference on System-Integrated Intelligence: New Challenges for Product and Production Engineering. Vol 26. ; 2016:465-472. doi:10.1016/j.protcy.2016.08.059","apa":"Eckstein, J., Peitz, S., Schäfer, K., Friedel, P., Köhler, U., Hessel von Molo, M., Ober-Blöbaum, S., & Dellnitz, M. (2016). A comparison of two predictive approaches to control the longitudinal dynamics of electric vehicles. Procedia Technology, 3rd International Conference on System-Integrated Intelligence: New Challenges for Product and Production Engineering, 26, 465–472. https://doi.org/10.1016/j.protcy.2016.08.059","bibtex":"@inproceedings{Eckstein_Peitz_Schäfer_Friedel_Köhler_Hessel von Molo_Ober-Blöbaum_Dellnitz_2016, title={A comparison of two predictive approaches to control the longitudinal dynamics of electric vehicles}, volume={26}, DOI={10.1016/j.protcy.2016.08.059}, booktitle={Procedia Technology, 3rd International Conference on System-Integrated Intelligence: New Challenges for Product and Production Engineering}, author={Eckstein, Julian and Peitz, Sebastian and Schäfer, Kai and Friedel, Patrick and Köhler, Ulrich and Hessel von Molo, Mirko and Ober-Blöbaum, Sina and Dellnitz, Michael}, year={2016}, pages={465–472} }","mla":"Eckstein, Julian, et al. “A Comparison of Two Predictive Approaches to Control the Longitudinal Dynamics of Electric Vehicles.” Procedia Technology, 3rd International Conference on System-Integrated Intelligence: New Challenges for Product and Production Engineering, vol. 26, 2016, pp. 465–72, doi:10.1016/j.protcy.2016.08.059."},"year":"2016","page":"465-472","user_id":"15694","title":"A comparison of two predictive approaches to control the longitudinal dynamics of electric vehicles","abstract":[{"lang":"eng","text":"In this contribution we compare two different approaches to the implementation of a Model Predictive Controller in an electric vehicle with respect to the quality of the solution and real-time applicability. The goal is to develop an intelligent cruise control in order to extend the vehicle range, i.e. to minimize energy consumption, by computing the optimal torque profile for a given track. On the one hand, a path-based linear model with strong simplifications regarding the vehicle dynamics is used. On the other hand, a nonlinear model is employed in which the dynamics of the mechanical and electrical subsystem are modeled."}],"status":"public","date_created":"2019-03-29T13:35:25Z","publication_status":"published","volume":26,"publication_identifier":{"issn":["2212-0173"]},"author":[{"last_name":"Eckstein","full_name":"Eckstein, Julian","first_name":"Julian"},{"orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian","id":"47427","last_name":"Peitz"},{"full_name":"Schäfer, Kai","first_name":"Kai","last_name":"Schäfer"},{"last_name":"Friedel","first_name":"Patrick","full_name":"Friedel, Patrick"},{"first_name":"Ulrich","full_name":"Köhler, Ulrich","last_name":"Köhler"},{"full_name":"Hessel von Molo, Mirko ","first_name":"Mirko ","last_name":"Hessel von Molo"},{"id":"16494","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"}],"department":[{"_id":"101"}],"publication":"Procedia Technology, 3rd International Conference on System-Integrated Intelligence: New Challenges for Product and Production Engineering"},{"user_id":"15701","title":"A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator","status":"public","date_created":"2020-04-15T09:08:34Z","publication_identifier":{"isbn":["9789810243593","9789812792617"]},"publication_status":"published","author":[{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"last_name":"Froyland","full_name":"Froyland, Gary","first_name":"Gary"},{"last_name":"Sertl","full_name":"Sertl, Stefan","first_name":"Stefan"}],"department":[{"_id":"101"}],"publication":"Equadiff 99","doi":"10.1142/9789812792617_0199","date_updated":"2022-01-06T06:52:52Z","_id":"16553","language":[{"iso":"eng"}],"citation":{"short":"M. Dellnitz, G. Froyland, S. Sertl, in: Equadiff 99, 2000.","ieee":"M. Dellnitz, G. Froyland, and S. Sertl, “A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator,” in Equadiff 99, 2000.","ama":"Dellnitz M, Froyland G, Sertl S. A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator. In: Equadiff 99. ; 2000. doi:10.1142/9789812792617_0199","apa":"Dellnitz, M., Froyland, G., & Sertl, S. (2000). A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator. In Equadiff 99. https://doi.org/10.1142/9789812792617_0199","chicago":"Dellnitz, Michael, Gary Froyland, and Stefan Sertl. “A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator.” In Equadiff 99, 2000. https://doi.org/10.1142/9789812792617_0199.","mla":"Dellnitz, Michael, et al. “A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator.” Equadiff 99, 2000, doi:10.1142/9789812792617_0199.","bibtex":"@inbook{Dellnitz_Froyland_Sertl_2000, title={A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator}, DOI={10.1142/9789812792617_0199}, booktitle={Equadiff 99}, author={Dellnitz, Michael and Froyland, Gary and Sertl, Stefan}, year={2000} }"},"type":"book_chapter","year":"2000"},{"doi":"10.1007/978-3-319-96104-0_2","date_updated":"2022-01-06T07:04:00Z","_id":"8750","conference":{"name":"NEO 2017: Numerical and Evolutionary Optimization"},"citation":{"short":"B. Gebken, S. Peitz, M. Dellnitz, in: Numerical and Evolutionary Optimization – NEO 2017, Cham, 2018.","ieee":"B. Gebken, S. Peitz, and M. Dellnitz, “A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems,” in Numerical and Evolutionary Optimization – NEO 2017, 2018.","apa":"Gebken, B., Peitz, S., & Dellnitz, M. (2018). A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems. In Numerical and Evolutionary Optimization – NEO 2017. Cham. https://doi.org/10.1007/978-3-319-96104-0_2","ama":"Gebken B, Peitz S, Dellnitz M. A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems. In: Numerical and Evolutionary Optimization – NEO 2017. Cham; 2018. doi:10.1007/978-3-319-96104-0_2","chicago":"Gebken, Bennet, Sebastian Peitz, and Michael Dellnitz. “A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems.” In Numerical and Evolutionary Optimization – NEO 2017. Cham, 2018. https://doi.org/10.1007/978-3-319-96104-0_2.","bibtex":"@inproceedings{Gebken_Peitz_Dellnitz_2018, place={Cham}, title={A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems}, DOI={10.1007/978-3-319-96104-0_2}, booktitle={Numerical and Evolutionary Optimization – NEO 2017}, author={Gebken, Bennet and Peitz, Sebastian and Dellnitz, Michael}, year={2018} }","mla":"Gebken, Bennet, et al. “A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems.” Numerical and Evolutionary Optimization – NEO 2017, 2018, doi:10.1007/978-3-319-96104-0_2."},"year":"2018","type":"conference","language":[{"iso":"eng"}],"title":"A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems","user_id":"47427","place":"Cham","abstract":[{"text":"In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained problems by using two active set strategies. Under some regularity assumptions on the problem, we show that accumulation points of our descent method satisfy a necessary condition for local Pareto optimality. Finally, we show the typical behavior of our method in a numerical example.","lang":"eng"}],"publication_status":"published","publication_identifier":{"issn":["1860-949X","1860-9503"],"isbn":["9783319961033","9783319961040"]},"status":"public","date_created":"2019-03-29T13:26:47Z","author":[{"full_name":"Gebken, Bennet","first_name":"Bennet","id":"32643","last_name":"Gebken"},{"full_name":"Peitz, Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","first_name":"Sebastian","id":"47427","last_name":"Peitz"},{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"}],"publication":"Numerical and Evolutionary Optimization – NEO 2017","department":[{"_id":"101"}]},{"status":"public","has_accepted_license":"1","date_created":"2024-02-13T09:35:26Z","author":[{"id":"56399","last_name":"Sonntag","full_name":"Sonntag, Konstantin","orcid":"https://orcid.org/0000-0003-3384-3496","first_name":"Konstantin"},{"full_name":"Gebken, Bennet","first_name":"Bennet","id":"32643","last_name":"Gebken"},{"last_name":"Müller","full_name":"Müller, Georg","first_name":"Georg"},{"first_name":"Sebastian","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","last_name":"Peitz","id":"47427"},{"last_name":"Volkwein","first_name":"Stefan","full_name":"Volkwein, Stefan"}],"department":[{"_id":"101"},{"_id":"655"}],"publication":"arXiv:2402.06376","user_id":"56399","title":"A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces","abstract":[{"lang":"eng","text":"The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points, where in each iteration, an approximation of the subdifferential is computed in an efficient manner and then used to compute a common descent direction for all objective functions. To prove convergence, we present some new optimality results for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these, we can show that every accumulation point of the sequence generated by our algorithm is Pareto critical under common assumptions. Computational efficiency for finding Pareto critical points is numerically demonstrated for multiobjective optimal control of an obstacle problem."}],"external_id":{"arxiv":["\t2402.06376"]},"language":[{"iso":"eng"}],"year":"2024","citation":{"mla":"Sonntag, Konstantin, et al. “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.” ArXiv:2402.06376, 2024.","bibtex":"@article{Sonntag_Gebken_Müller_Peitz_Volkwein_2024, title={A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces}, journal={arXiv:2402.06376}, author={Sonntag, Konstantin and Gebken, Bennet and Müller, Georg and Peitz, Sebastian and Volkwein, Stefan}, year={2024} }","chicago":"Sonntag, Konstantin, Bennet Gebken, Georg Müller, Sebastian Peitz, and Stefan Volkwein. “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.” ArXiv:2402.06376, 2024.","ama":"Sonntag K, Gebken B, Müller G, Peitz S, Volkwein S. A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces. arXiv:240206376. Published online 2024.","apa":"Sonntag, K., Gebken, B., Müller, G., Peitz, S., & Volkwein, S. (2024). A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces. In arXiv:2402.06376.","ieee":"K. Sonntag, B. Gebken, G. Müller, S. Peitz, and S. Volkwein, “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces,” arXiv:2402.06376. 2024.","short":"K. Sonntag, B. Gebken, G. Müller, S. Peitz, S. Volkwein, ArXiv:2402.06376 (2024)."},"type":"preprint","main_file_link":[{"url":"https://arxiv.org/abs/2402.06376","open_access":"1"}],"oa":"1","date_updated":"2024-02-21T10:21:03Z","_id":"51334"},{"user_id":"15701","title":"A Memetic PSO Algorithm for Scalar Optimization Problems","date_created":"2020-04-16T10:00:10Z","status":"public","publication_identifier":{"isbn":["1424407087"]},"publication_status":"published","publication":"2007 IEEE Swarm Intelligence Symposium","department":[{"_id":"101"}],"author":[{"full_name":"Schütze, Oliver","first_name":"Oliver","last_name":"Schütze"},{"full_name":"Talbi, El-ghazali","first_name":"El-ghazali","last_name":"Talbi"},{"last_name":"Pulido","first_name":"Gregorio Toscano","full_name":"Pulido, Gregorio Toscano"},{"last_name":"Coello","first_name":"Carlos Coello","full_name":"Coello, Carlos Coello"},{"full_name":"Santana-Quintero, Luis Vicente","first_name":"Luis Vicente","last_name":"Santana-Quintero"}],"doi":"10.1109/sis.2007.368036","date_updated":"2022-01-06T06:52:54Z","_id":"16666","language":[{"iso":"eng"}],"citation":{"mla":"Schütze, Oliver, et al. “A Memetic PSO Algorithm for Scalar Optimization Problems.” 2007 IEEE Swarm Intelligence Symposium, 2007, doi:10.1109/sis.2007.368036.","bibtex":"@inproceedings{Schütze_Talbi_Pulido_Coello_Santana-Quintero_2007, title={A Memetic PSO Algorithm for Scalar Optimization Problems}, DOI={10.1109/sis.2007.368036}, booktitle={2007 IEEE Swarm Intelligence Symposium}, author={Schütze, Oliver and Talbi, El-ghazali and Pulido, Gregorio Toscano and Coello, Carlos Coello and Santana-Quintero, Luis Vicente}, year={2007} }","chicago":"Schütze, Oliver, El-ghazali Talbi, Gregorio Toscano Pulido, Carlos Coello Coello, and Luis Vicente Santana-Quintero. “A Memetic PSO Algorithm for Scalar Optimization Problems.” In 2007 IEEE Swarm Intelligence Symposium, 2007. https://doi.org/10.1109/sis.2007.368036.","apa":"Schütze, O., Talbi, E., Pulido, G. T., Coello, C. C., & Santana-Quintero, L. V. (2007). A Memetic PSO Algorithm for Scalar Optimization Problems. In 2007 IEEE Swarm Intelligence Symposium. https://doi.org/10.1109/sis.2007.368036","ama":"Schütze O, Talbi E, Pulido GT, Coello CC, Santana-Quintero LV. A Memetic PSO Algorithm for Scalar Optimization Problems. In: 2007 IEEE Swarm Intelligence Symposium. ; 2007. doi:10.1109/sis.2007.368036","ieee":"O. Schütze, E. Talbi, G. T. Pulido, C. C. Coello, and L. V. Santana-Quintero, “A Memetic PSO Algorithm for Scalar Optimization Problems,” in 2007 IEEE Swarm Intelligence Symposium, 2007.","short":"O. Schütze, E. Talbi, G.T. Pulido, C.C. Coello, L.V. Santana-Quintero, in: 2007 IEEE Swarm Intelligence Symposium, 2007."},"year":"2007","type":"conference"},{"user_id":"15701","title":"A multi-objective approach to the design of low thrust space trajectories using optimal control","status":"public","date_created":"2020-04-16T05:05:17Z","publication_status":"published","publication_identifier":{"issn":["0923-2958","1572-9478"]},"author":[{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"},{"last_name":"Post","full_name":"Post, Marcus","first_name":"Marcus"},{"last_name":"Schütze","first_name":"Oliver","full_name":"Schütze, Oliver"},{"last_name":"Thiere","first_name":"Bianca","full_name":"Thiere, Bianca"}],"department":[{"_id":"101"}],"publication":"Celestial Mechanics and Dynamical Astronomy","doi":"10.1007/s10569-009-9229-y","_id":"16574","date_updated":"2022-01-06T06:52:52Z","language":[{"iso":"eng"}],"citation":{"short":"M. Dellnitz, S. Ober-Blöbaum, M. Post, O. Schütze, B. Thiere, Celestial Mechanics and Dynamical Astronomy (2009) 33–59.","ieee":"M. Dellnitz, S. Ober-Blöbaum, M. Post, O. Schütze, and B. Thiere, “A multi-objective approach to the design of low thrust space trajectories using optimal control,” Celestial Mechanics and Dynamical Astronomy, pp. 33–59, 2009.","chicago":"Dellnitz, Michael, Sina Ober-Blöbaum, Marcus Post, Oliver Schütze, and Bianca Thiere. “A Multi-Objective Approach to the Design of Low Thrust Space Trajectories Using Optimal Control.” Celestial Mechanics and Dynamical Astronomy, 2009, 33–59. https://doi.org/10.1007/s10569-009-9229-y.","apa":"Dellnitz, M., Ober-Blöbaum, S., Post, M., Schütze, O., & Thiere, B. (2009). A multi-objective approach to the design of low thrust space trajectories using optimal control. Celestial Mechanics and Dynamical Astronomy, 33–59. https://doi.org/10.1007/s10569-009-9229-y","ama":"Dellnitz M, Ober-Blöbaum S, Post M, Schütze O, Thiere B. A multi-objective approach to the design of low thrust space trajectories using optimal control. Celestial Mechanics and Dynamical Astronomy. 2009:33-59. doi:10.1007/s10569-009-9229-y","mla":"Dellnitz, Michael, et al. “A Multi-Objective Approach to the Design of Low Thrust Space Trajectories Using Optimal Control.” Celestial Mechanics and Dynamical Astronomy, 2009, pp. 33–59, doi:10.1007/s10569-009-9229-y.","bibtex":"@article{Dellnitz_Ober-Blöbaum_Post_Schütze_Thiere_2009, title={A multi-objective approach to the design of low thrust space trajectories using optimal control}, DOI={10.1007/s10569-009-9229-y}, journal={Celestial Mechanics and Dynamical Astronomy}, author={Dellnitz, Michael and Ober-Blöbaum, Sina and Post, Marcus and Schütze, Oliver and Thiere, Bianca}, year={2009}, pages={33–59} }"},"type":"journal_article","year":"2009","page":"33-59"},{"title":"A multiobjective MPC approach for autonomously driven electric vehicles","publication_status":"published","publication_identifier":{"issn":["2405-8963"]},"department":[{"_id":"101"}],"doi":"10.1016/j.ifacol.2017.08.1526","date_updated":"2022-01-21T13:58:41Z","language":[{"iso":"eng"}],"user_id":"15694","article_type":"original","abstract":[{"text":"We present a new algorithm for model predictive control of non-linear systems with respect to multiple, conflicting objectives. The idea is to provide a possibility to change the objective in real-time, e.g. as a reaction to changes in the environment or the system state itself. The algorithm utilises elements from various well-established concepts, namely multiobjective optimal control, economic as well as explicit model predictive control and motion planning with motion primitives. In order to realise real-time applicability, we split the computation into an online and an offline phase and we utilise symmetries in the open-loop optimal control problem to reduce the number of multiobjective optimal control problems that need to be solved in the offline phase. The results are illustrated using the example of an electric vehicle where the longitudinal dynamics are controlled with respect to the concurrent objectives arrival time and energy consumption.","lang":"eng"}],"status":"public","date_created":"2019-03-29T13:32:46Z","volume":50,"author":[{"id":"47427","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian"},{"full_name":"Schäfer, Kai","first_name":"Kai","last_name":"Schäfer"},{"last_name":"Ober-Blöbaum","id":"16494","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"first_name":"Julian","full_name":"Eckstein, Julian","last_name":"Eckstein"},{"full_name":"Köhler, Ulrich","first_name":"Ulrich","last_name":"Köhler"},{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"}],"publication":"Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)","issue":"1","_id":"8756","intvolume":" 50","conference":{"end_date":"2017-07-14","start_date":"2017-07-09"},"type":"journal_article","citation":{"ieee":"S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, and M. Dellnitz, “A multiobjective MPC approach for autonomously driven electric vehicles,” Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC), vol. 50, no. 1, pp. 8674–8679, 2017, doi: 10.1016/j.ifacol.2017.08.1526.","short":"S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, M. Dellnitz, Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC) 50 (2017) 8674–8679.","bibtex":"@article{Peitz_Schäfer_Ober-Blöbaum_Eckstein_Köhler_Dellnitz_2017, title={A multiobjective MPC approach for autonomously driven electric vehicles}, volume={50}, DOI={10.1016/j.ifacol.2017.08.1526}, number={1}, journal={Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)}, author={Peitz, Sebastian and Schäfer, Kai and Ober-Blöbaum, Sina and Eckstein, Julian and Köhler, Ulrich and Dellnitz, Michael}, year={2017}, pages={8674–8679} }","mla":"Peitz, Sebastian, et al. “A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles.” Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC), vol. 50, no. 1, 2017, pp. 8674–79, doi:10.1016/j.ifacol.2017.08.1526.","ama":"Peitz S, Schäfer K, Ober-Blöbaum S, Eckstein J, Köhler U, Dellnitz M. 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Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC), 50(1), 8674–8679. https://doi.org/10.1016/j.ifacol.2017.08.1526","chicago":"Peitz, Sebastian, Kai Schäfer, Sina Ober-Blöbaum, Julian Eckstein, Ulrich Köhler, and Michael Dellnitz. “A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles.” Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC) 50, no. 1 (2017): 8674–79. https://doi.org/10.1016/j.ifacol.2017.08.1526."},"year":"2017","page":"8674-8679"},{"publication_status":"published","publication_identifier":{"issn":["2405-8963"]},"date_created":"2020-04-16T09:30:56Z","status":"public","department":[{"_id":"101"}],"publication":"IFAC-PapersOnLine","author":[{"full_name":"Peitz, Sebastian","first_name":"Sebastian","last_name":"Peitz"},{"first_name":"Kai","full_name":"Schäfer, Kai","last_name":"Schäfer"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"},{"first_name":"Julian","full_name":"Eckstein, Julian","last_name":"Eckstein"},{"last_name":"Köhler","first_name":"Ulrich","full_name":"Köhler, Ulrich"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"title":"A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This research was funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (it’s OWL).","user_id":"15701","page":"8674-8679","type":"journal_article","year":"2017","citation":{"short":"S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, M. Dellnitz, IFAC-PapersOnLine (2017) 8674–8679.","ieee":"S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, and M. Dellnitz, “A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This research was funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (it’s OWL).,” IFAC-PapersOnLine, pp. 8674–8679, 2017.","ama":"Peitz S, Schäfer K, Ober-Blöbaum S, Eckstein J, Köhler U, Dellnitz M. A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This research was funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (it’s OWL). IFAC-PapersOnLine. 2017:8674-8679. doi:10.1016/j.ifacol.2017.08.1526","apa":"Peitz, S., Schäfer, K., Ober-Blöbaum, S., Eckstein, J., Köhler, U., & Dellnitz, M. (2017). A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This research was funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (it’s OWL). IFAC-PapersOnLine, 8674–8679. https://doi.org/10.1016/j.ifacol.2017.08.1526","chicago":"Peitz, Sebastian, Kai Schäfer, Sina Ober-Blöbaum, Julian Eckstein, Ulrich Köhler, and Michael Dellnitz. “A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This Research Was Funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (It’s OWL).” IFAC-PapersOnLine, 2017, 8674–79. https://doi.org/10.1016/j.ifacol.2017.08.1526.","bibtex":"@article{Peitz_Schäfer_Ober-Blöbaum_Eckstein_Köhler_Dellnitz_2017, title={A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This research was funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (it’s OWL).}, DOI={10.1016/j.ifacol.2017.08.1526}, journal={IFAC-PapersOnLine}, author={Peitz, Sebastian and Schäfer, Kai and Ober-Blöbaum, Sina and Eckstein, Julian and Köhler, Ulrich and Dellnitz, Michael}, year={2017}, pages={8674–8679} }","mla":"Peitz, Sebastian, et al. “A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This Research Was Funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (It’s OWL).” IFAC-PapersOnLine, 2017, pp. 8674–79, doi:10.1016/j.ifacol.2017.08.1526."},"language":[{"iso":"eng"}],"doi":"10.1016/j.ifacol.2017.08.1526","date_updated":"2022-01-06T06:52:53Z","_id":"16657"},{"title":"A multiobjective optimization approach for optimal control problems of mechanical systems with uncertainties","user_id":"15701","publication_identifier":{"isbn":["9783033039629"]},"publication_status":"published","date_created":"2020-04-16T09:01:37Z","status":"public","publication":"2013 European Control Conference (ECC)","department":[{"_id":"101"}],"author":[{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"},{"first_name":"Albert","full_name":"Seifried, Albert","last_name":"Seifried"}],"doi":"10.23919/ecc.2013.6669594","date_updated":"2022-01-06T06:52:53Z","_id":"16643","citation":{"bibtex":"@inproceedings{Ober-Blöbaum_Seifried_2013, title={A multiobjective optimization approach for optimal control problems of mechanical systems with uncertainties}, DOI={10.23919/ecc.2013.6669594}, booktitle={2013 European Control Conference (ECC)}, author={Ober-Blöbaum, Sina and Seifried, Albert}, year={2013} }","mla":"Ober-Blöbaum, Sina, and Albert Seifried. “A Multiobjective Optimization Approach for Optimal Control Problems of Mechanical Systems with Uncertainties.” 2013 European Control Conference (ECC), 2013, doi:10.23919/ecc.2013.6669594.","apa":"Ober-Blöbaum, S., & Seifried, A. 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Seifried, in: 2013 European Control Conference (ECC), 2013."},"year":"2013","type":"conference","language":[{"iso":"eng"}]},{"user_id":"15701","title":"A new approach for online multiobjective optimization of mechatronic systems","publication":"International Journal on Software Tools for Technology Transfer","department":[{"_id":"101"}],"author":[{"first_name":"Katrin","full_name":"Witting, Katrin","last_name":"Witting"},{"full_name":"Schulz, Bernd","first_name":"Bernd","last_name":"Schulz"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"},{"first_name":"Joachim","full_name":"Böcker, Joachim","last_name":"Böcker"},{"last_name":"Fröhleke","full_name":"Fröhleke, Norbert","first_name":"Norbert"}],"date_created":"2020-04-16T10:22:02Z","status":"public","publication_status":"published","publication_identifier":{"issn":["1433-2779","1433-2787"]},"date_updated":"2022-01-06T06:52:54Z","_id":"16678","doi":"10.1007/s10009-008-0066-1","language":[{"iso":"eng"}],"page":"223-231","citation":{"chicago":"Witting, Katrin, Bernd Schulz, Michael Dellnitz, Joachim Böcker, and Norbert Fröhleke. “A New Approach for Online Multiobjective Optimization of Mechatronic Systems.” International Journal on Software Tools for Technology Transfer, 2008, 223–31. https://doi.org/10.1007/s10009-008-0066-1.","ama":"Witting K, Schulz B, Dellnitz M, Böcker J, Fröhleke N. 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Fröhleke, “A new approach for online multiobjective optimization of mechatronic systems,” International Journal on Software Tools for Technology Transfer, pp. 223–231, 2008."},"year":"2008","type":"journal_article"},{"doi":"10.1007/3-540-36970-8_36","_id":"16664","date_updated":"2022-01-06T06:52:54Z","language":[{"iso":"eng"}],"citation":{"bibtex":"@inbook{Schütze_2003, place={Berlin, Heidelberg}, title={A New Data Structure for the Nondominance Problem in Multi-objective Optimization}, DOI={10.1007/3-540-36970-8_36}, booktitle={Lecture Notes in Computer Science}, author={Schütze, Oliver}, year={2003} }","mla":"Schütze, Oliver. “A New Data Structure for the Nondominance Problem in Multi-Objective Optimization.” Lecture Notes in Computer Science, 2003, doi:10.1007/3-540-36970-8_36.","apa":"Schütze, O. (2003). A New Data Structure for the Nondominance Problem in Multi-objective Optimization. In Lecture Notes in Computer Science. Berlin, Heidelberg. https://doi.org/10.1007/3-540-36970-8_36","ama":"Schütze O. A New Data Structure for the Nondominance Problem in Multi-objective Optimization. In: Lecture Notes in Computer Science. Berlin, Heidelberg; 2003. doi:10.1007/3-540-36970-8_36","chicago":"Schütze, Oliver. “A New Data Structure for the Nondominance Problem in Multi-Objective Optimization.” In Lecture Notes in Computer Science. Berlin, Heidelberg, 2003. https://doi.org/10.1007/3-540-36970-8_36.","ieee":"O. Schütze, “A New Data Structure for the Nondominance Problem in Multi-objective Optimization,” in Lecture Notes in Computer Science, Berlin, Heidelberg, 2003.","short":"O. Schütze, in: Lecture Notes in Computer Science, Berlin, Heidelberg, 2003."},"type":"book_chapter","year":"2003","user_id":"15701","title":"A New Data Structure for the Nondominance Problem in Multi-objective Optimization","place":"Berlin, Heidelberg","date_created":"2020-04-16T09:57:05Z","status":"public","publication_identifier":{"isbn":["9783540018698","9783540369707"],"issn":["0302-9743"]},"publication_status":"published","department":[{"_id":"101"}],"publication":"Lecture Notes in Computer Science","author":[{"last_name":"Schütze","full_name":"Schütze, Oliver","first_name":"Oliver"}]},{"department":[{"_id":"101"}],"keyword":["Applied Mathematics","Computational Mathematics","Control and Optimization"],"publication":"Computational Optimization and Applications","author":[{"id":"32643","last_name":"Gebken","full_name":"Gebken, Bennet","first_name":"Bennet"}],"publisher":"Springer Science and Business Media LLC","date_created":"2024-02-07T07:23:23Z","status":"public","publication_identifier":{"issn":["0926-6003","1573-2894"]},"publication_status":"published","abstract":[{"lang":"eng","text":"AbstractApproximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions."}],"user_id":"32643","title":"A note on the convergence of deterministic gradient sampling in nonsmooth optimization","language":[{"iso":"eng"}],"year":"2024","type":"journal_article","citation":{"ieee":"B. Gebken, “A note on the convergence of deterministic gradient sampling in nonsmooth optimization,” Computational Optimization and Applications, 2024, doi: 10.1007/s10589-024-00552-0.","short":"B. Gebken, Computational Optimization and Applications (2024).","mla":"Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling in Nonsmooth Optimization.” Computational Optimization and Applications, Springer Science and Business Media LLC, 2024, doi:10.1007/s10589-024-00552-0.","bibtex":"@article{Gebken_2024, title={A note on the convergence of deterministic gradient sampling in nonsmooth optimization}, DOI={10.1007/s10589-024-00552-0}, journal={Computational Optimization and Applications}, publisher={Springer Science and Business Media LLC}, author={Gebken, Bennet}, year={2024} }","ama":"Gebken B. A note on the convergence of deterministic gradient sampling in nonsmooth optimization. Computational Optimization and Applications. Published online 2024. doi:10.1007/s10589-024-00552-0","apa":"Gebken, B. (2024). A note on the convergence of deterministic gradient sampling in nonsmooth optimization. Computational Optimization and Applications. https://doi.org/10.1007/s10589-024-00552-0","chicago":"Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling in Nonsmooth Optimization.” Computational Optimization and Applications, 2024. https://doi.org/10.1007/s10589-024-00552-0."},"date_updated":"2024-02-08T08:05:54Z","_id":"51208","doi":"10.1007/s10589-024-00552-0"},{"page":"1067-1075","type":"journal_article","citation":{"ieee":"M. Dellnitz and I. Melbourne, “A note on the shadowing lemma and symmetric periodic points,” Nonlinearity, pp. 1067–1075, 1995.","short":"M. Dellnitz, I. Melbourne, Nonlinearity (1995) 1067–1075.","bibtex":"@article{Dellnitz_Melbourne_1995, title={A note on the shadowing lemma and symmetric periodic points}, DOI={10.1088/0951-7715/8/6/010}, journal={Nonlinearity}, author={Dellnitz, M and Melbourne, I}, year={1995}, pages={1067–1075} }","mla":"Dellnitz, M., and I. 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Nonlinearity. 1995:1067-1075. doi:10.1088/0951-7715/8/6/010","chicago":"Dellnitz, M, and I Melbourne. “A Note on the Shadowing Lemma and Symmetric Periodic Points.” Nonlinearity, 1995, 1067–75. https://doi.org/10.1088/0951-7715/8/6/010."},"year":"1995","language":[{"iso":"eng"}],"date_updated":"2022-01-06T06:52:52Z","_id":"16542","doi":"10.1088/0951-7715/8/6/010","publication":"Nonlinearity","department":[{"_id":"101"}],"author":[{"last_name":"Dellnitz","full_name":"Dellnitz, M","first_name":"M"},{"last_name":"Melbourne","full_name":"Melbourne, I","first_name":"I"}],"publication_status":"published","publication_identifier":{"issn":["0951-7715","1361-6544"]},"date_created":"2020-04-15T08:46:30Z","status":"public","title":"A note on the shadowing lemma and symmetric periodic points","user_id":"15701"},{"year":"2023","citation":{"ieee":"S. von der Gracht, E. Nijholt, and B. Rink, “A parametrisation method for high-order phase reduction in coupled oscillator networks,” arXiv:2306.03320. .","short":"S. von der Gracht, E. Nijholt, B. Rink, ArXiv:2306.03320 (n.d.).","mla":"von der Gracht, Sören, et al. “A Parametrisation Method for High-Order Phase Reduction in Coupled Oscillator Networks.” ArXiv:2306.03320.","bibtex":"@article{von der Gracht_Nijholt_Rink, title={A parametrisation method for high-order phase reduction in coupled oscillator networks}, journal={arXiv:2306.03320}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob} }","ama":"von der Gracht S, Nijholt E, Rink B. A parametrisation method for high-order phase reduction in coupled oscillator networks. arXiv:230603320.","apa":"von der Gracht, S., Nijholt, E., & Rink, B. (n.d.). A parametrisation method for high-order phase reduction in coupled oscillator networks. In arXiv:2306.03320.","chicago":"Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “A Parametrisation Method for High-Order Phase Reduction in Coupled Oscillator Networks.” ArXiv:2306.03320, n.d."},"type":"preprint","page":"29","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/pdf/2306.03320"}],"_id":"45498","date_updated":"2023-06-07T07:59:06Z","publication_status":"submitted","status":"public","date_created":"2023-06-07T07:57:28Z","author":[{"last_name":"von der Gracht","id":"97359","first_name":"Sören","orcid":"0000-0002-8054-2058","full_name":"von der Gracht, Sören"},{"last_name":"Nijholt","full_name":"Nijholt, Eddie","first_name":"Eddie"},{"last_name":"Rink","full_name":"Rink, Bob","first_name":"Bob"}],"department":[{"_id":"101"}],"publication":"arXiv:2306.03320","title":"A parametrisation method for high-order phase reduction in coupled oscillator networks","user_id":"97359","external_id":{"arxiv":["2306.03320"]},"abstract":[{"text":"We present a novel method for high-order phase reduction in networks of\r\nweakly coupled oscillators and, more generally, perturbations of reducible\r\nnormally hyperbolic (quasi-)periodic tori. Our method works by computing an\r\nasymptotic expansion for an embedding of the perturbed invariant torus, as well\r\nas for the reduced phase dynamics in local coordinates. Both can be determined\r\nto arbitrary degrees of accuracy, and we show that the phase dynamics may\r\ndirectly be obtained in normal form. We apply the method to predict remote\r\nsynchronisation in a chain of coupled Stuart-Landau oscillators.","lang":"eng"}]},{"date_created":"2020-04-15T08:17:18Z","status":"public","publication_identifier":{"issn":["1536-0040"]},"publication_status":"published","department":[{"_id":"101"}],"publication":"SIAM Journal on Applied Dynamical Systems","author":[{"last_name":"Day","full_name":"Day, S.","first_name":"S."},{"first_name":"O.","full_name":"Junge, O.","last_name":"Junge"},{"last_name":"Mischaikow","full_name":"Mischaikow, K.","first_name":"K."}],"user_id":"15701","title":"A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems","language":[{"iso":"eng"}],"page":"117-160","type":"journal_article","year":"2004","citation":{"mla":"Day, S., et al. “A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems.” SIAM Journal on Applied Dynamical Systems, 2004, pp. 117–60, doi:10.1137/030600210.","bibtex":"@article{Day_Junge_Mischaikow_2004, title={A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems}, DOI={10.1137/030600210}, journal={SIAM Journal on Applied Dynamical Systems}, author={Day, S. and Junge, O. and Mischaikow, K.}, year={2004}, pages={117–160} }","apa":"Day, S., Junge, O., & Mischaikow, K. (2004). A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems. SIAM Journal on Applied Dynamical Systems, 117–160. https://doi.org/10.1137/030600210","ama":"Day S, Junge O, Mischaikow K. A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems. SIAM Journal on Applied Dynamical Systems. 2004:117-160. doi:10.1137/030600210","chicago":"Day, S., O. Junge, and K. Mischaikow. “A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems.” SIAM Journal on Applied Dynamical Systems, 2004, 117–60. https://doi.org/10.1137/030600210.","ieee":"S. Day, O. Junge, and K. Mischaikow, “A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems,” SIAM Journal on Applied Dynamical Systems, pp. 117–160, 2004.","short":"S. Day, O. Junge, K. Mischaikow, SIAM Journal on Applied Dynamical Systems (2004) 117–160."},"doi":"10.1137/030600210","date_updated":"2022-01-06T06:52:52Z","_id":"16527"},{"author":[{"last_name":"Junge","full_name":"Junge, Oliver","first_name":"Oliver"},{"first_name":"Hinke M.","full_name":"Osinga, Hinke M.","last_name":"Osinga"}],"publication":"ESAIM: Control, Optimisation and Calculus of Variations","department":[{"_id":"101"}],"status":"public","date_created":"2020-04-16T08:11:16Z","publication_status":"published","publication_identifier":{"issn":["1292-8119","1262-3377"]},"user_id":"15701","title":"A set oriented approach to global optimal control","type":"journal_article","year":"2004","citation":{"short":"O. Junge, H.M. Osinga, ESAIM: Control, Optimisation and Calculus of Variations (2004) 259–270.","ieee":"O. Junge and H. M. Osinga, “A set oriented approach to global optimal control,” ESAIM: Control, Optimisation and Calculus of Variations, pp. 259–270, 2004.","chicago":"Junge, Oliver, and Hinke M. Osinga. “A Set Oriented Approach to Global Optimal Control.” ESAIM: Control, Optimisation and Calculus of Variations, 2004, 259–70. https://doi.org/10.1051/cocv:2004006.","apa":"Junge, O., & Osinga, H. M. (2004). A set oriented approach to global optimal control. ESAIM: Control, Optimisation and Calculus of Variations, 259–270. https://doi.org/10.1051/cocv:2004006","ama":"Junge O, Osinga HM. A set oriented approach to global optimal control. ESAIM: Control, Optimisation and Calculus of Variations. 2004:259-270. doi:10.1051/cocv:2004006","mla":"Junge, Oliver, and Hinke M. Osinga. “A Set Oriented Approach to Global Optimal Control.” ESAIM: Control, Optimisation and Calculus of Variations, 2004, pp. 259–70, doi:10.1051/cocv:2004006.","bibtex":"@article{Junge_Osinga_2004, title={A set oriented approach to global optimal control}, DOI={10.1051/cocv:2004006}, journal={ESAIM: Control, Optimisation and Calculus of Variations}, author={Junge, Oliver and Osinga, Hinke M.}, year={2004}, pages={259–270} }"},"page":"259-270","_id":"16619","date_updated":"2022-01-06T06:52:53Z","doi":"10.1051/cocv:2004006"},{"date_updated":"2022-01-06T06:52:53Z","_id":"16613","doi":"10.1016/j.sysconle.2004.08.005","page":"169-180","citation":{"chicago":"Grüne, Lars, and Oliver Junge. “A Set Oriented Approach to Optimal Feedback Stabilization.” Systems & Control Letters, 2005, 169–80. https://doi.org/10.1016/j.sysconle.2004.08.005.","apa":"Grüne, L., & Junge, O. (2005). A set oriented approach to optimal feedback stabilization. Systems & Control Letters, 169–180. https://doi.org/10.1016/j.sysconle.2004.08.005","ama":"Grüne L, Junge O. A set oriented approach to optimal feedback stabilization. Systems & Control Letters. 2005:169-180. doi:10.1016/j.sysconle.2004.08.005","bibtex":"@article{Grüne_Junge_2005, title={A set oriented approach to optimal feedback stabilization}, DOI={10.1016/j.sysconle.2004.08.005}, journal={Systems & Control Letters}, author={Grüne, Lars and Junge, Oliver}, year={2005}, pages={169–180} }","mla":"Grüne, Lars, and Oliver Junge. “A Set Oriented Approach to Optimal Feedback Stabilization.” Systems & Control Letters, 2005, pp. 169–80, doi:10.1016/j.sysconle.2004.08.005.","short":"L. Grüne, O. Junge, Systems & Control Letters (2005) 169–180.","ieee":"L. Grüne and O. Junge, “A set oriented approach to optimal feedback stabilization,” Systems & Control Letters, pp. 169–180, 2005."},"year":"2005","type":"journal_article","language":[{"iso":"eng"}],"title":"A set oriented approach to optimal feedback stabilization","user_id":"15701","publication":"Systems & Control Letters","department":[{"_id":"101"}],"author":[{"last_name":"Grüne","first_name":"Lars","full_name":"Grüne, Lars"},{"last_name":"Junge","full_name":"Junge, Oliver","first_name":"Oliver"}],"publication_status":"published","publication_identifier":{"issn":["0167-6911"]},"date_created":"2020-04-16T08:04:26Z","status":"public"},{"user_id":"15701","title":"A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty","status":"public","date_created":"2020-04-16T05:39:17Z","publication_status":"published","publication_identifier":{"issn":["1536-0040"]},"author":[{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"first_name":"Stefan","full_name":"Klus, Stefan","last_name":"Klus"},{"first_name":"Adrian","full_name":"Ziessler, Adrian","last_name":"Ziessler"}],"department":[{"_id":"101"}],"publication":"SIAM Journal on Applied Dynamical Systems","doi":"10.1137/16m1072735","_id":"16581","date_updated":"2022-01-06T06:52:52Z","language":[{"iso":"eng"}],"citation":{"chicago":"Dellnitz, Michael, Stefan Klus, and Adrian Ziessler. “A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty.” SIAM Journal on Applied Dynamical Systems, 2017, 120–38. https://doi.org/10.1137/16m1072735.","ama":"Dellnitz M, Klus S, Ziessler A. A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty. SIAM Journal on Applied Dynamical Systems. 2017:120-138. doi:10.1137/16m1072735","apa":"Dellnitz, M., Klus, S., & Ziessler, A. (2017). A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty. SIAM Journal on Applied Dynamical Systems, 120–138. https://doi.org/10.1137/16m1072735","bibtex":"@article{Dellnitz_Klus_Ziessler_2017, title={A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty}, DOI={10.1137/16m1072735}, journal={SIAM Journal on Applied Dynamical Systems}, author={Dellnitz, Michael and Klus, Stefan and Ziessler, Adrian}, year={2017}, pages={120–138} }","mla":"Dellnitz, Michael, et al. “A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty.” SIAM Journal on Applied Dynamical Systems, 2017, pp. 120–38, doi:10.1137/16m1072735.","short":"M. Dellnitz, S. Klus, A. Ziessler, SIAM Journal on Applied Dynamical Systems (2017) 120–138.","ieee":"M. Dellnitz, S. Klus, and A. Ziessler, “A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty,” SIAM Journal on Applied Dynamical Systems, pp. 120–138, 2017."},"year":"2017","type":"journal_article","page":"120-138"},{"main_file_link":[{"url":"https://epubs.siam.org/doi/epdf/10.1137/19M1247139","open_access":"1"}],"language":[{"iso":"eng"}],"page":"705-723","year":"2020","type":"journal_article","citation":{"ieee":"R. Gerlach, A. Ziessler, B. Eckhardt, and M. Dellnitz, “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors,” SIAM Journal on Applied Dynamical Systems, pp. 705–723, 2020, doi: 10.1137/19m1247139.","bibtex":"@article{Gerlach_Ziessler_Eckhardt_Dellnitz_2020, title={A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors}, DOI={10.1137/19m1247139}, journal={SIAM Journal on Applied Dynamical Systems}, author={Gerlach, Raphael and Ziessler, Adrian and Eckhardt, Bruno and Dellnitz, Michael}, year={2020}, pages={705–723} }","mla":"Gerlach, Raphael, et al. “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors.” SIAM Journal on Applied Dynamical Systems, 2020, pp. 705–23, doi:10.1137/19m1247139.","apa":"Gerlach, R., Ziessler, A., Eckhardt, B., & Dellnitz, M. (2020). A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors. SIAM Journal on Applied Dynamical Systems, 705–723. https://doi.org/10.1137/19m1247139","short":"R. Gerlach, A. Ziessler, B. Eckhardt, M. Dellnitz, SIAM Journal on Applied Dynamical Systems (2020) 705–723.","ama":"Gerlach R, Ziessler A, Eckhardt B, Dellnitz M. A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors. SIAM Journal on Applied Dynamical Systems. Published online 2020:705-723. doi:10.1137/19m1247139","chicago":"Gerlach, Raphael, Adrian Ziessler, Bruno Eckhardt, and Michael Dellnitz. “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors.” SIAM Journal on Applied Dynamical Systems, 2020, 705–23. https://doi.org/10.1137/19m1247139."},"_id":"16710","date_updated":"2022-06-21T09:18:46Z","oa":"1","doi":"10.1137/19m1247139","publication":"SIAM Journal on Applied Dynamical Systems","department":[{"_id":"101"}],"author":[{"first_name":"Raphael","full_name":"Gerlach, Raphael","last_name":"Gerlach","id":"32655"},{"first_name":"Adrian","full_name":"Ziessler, Adrian","last_name":"Ziessler"},{"full_name":"Eckhardt, Bruno","first_name":"Bruno","last_name":"Eckhardt"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"date_created":"2020-04-16T14:05:41Z","status":"public","publication_identifier":{"issn":["1536-0040"]},"publication_status":"published","abstract":[{"lang":"eng","text":"In this work we present a set-oriented path following method for the computation of relative global\r\nattractors of parameter-dependent dynamical systems. We start with an initial approximation of the\r\nrelative global attractor for a fixed parameter λ0 computed by a set-oriented subdivision method.\r\nBy using previously obtained approximations of the parameter-dependent relative global attractor\r\nwe can track it with respect to a one-dimensional parameter λ > λ0 without restarting the whole\r\nsubdivision procedure. We illustrate the feasibility of the set-oriented path following method by\r\nexploring the dynamics in low-dimensional models for shear flows during the transition to turbulence\r\nand of large-scale atmospheric regime changes .\r\n"}],"user_id":"32655","title":"A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors"},{"doi":"10.1007/s002110050240","_id":"17015","date_updated":"2022-01-06T06:53:02Z","intvolume":" 75","language":[{"iso":"eng"}],"year":"1997","type":"journal_article","citation":{"bibtex":"@article{Dellnitz_Hohmann_1997, title={A subdivision algorithm for the computation of unstable manifolds and global attractors}, volume={75}, DOI={10.1007/s002110050240}, journal={Numerische Mathematik}, author={Dellnitz, Michael and Hohmann, Andreas}, year={1997}, pages={293–317} }","mla":"Dellnitz, Michael, and Andreas Hohmann. “A Subdivision Algorithm for the Computation of Unstable Manifolds and Global Attractors.” Numerische Mathematik, vol. 75, 1997, pp. 293–317, doi:10.1007/s002110050240.","chicago":"Dellnitz, Michael, and Andreas Hohmann. “A Subdivision Algorithm for the Computation of Unstable Manifolds and Global Attractors.” Numerische Mathematik 75 (1997): 293–317. https://doi.org/10.1007/s002110050240.","apa":"Dellnitz, M., & Hohmann, A. (1997). A subdivision algorithm for the computation of unstable manifolds and global attractors. Numerische Mathematik, 75, 293–317. https://doi.org/10.1007/s002110050240","ama":"Dellnitz M, Hohmann A. A subdivision algorithm for the computation of unstable manifolds and global attractors. Numerische Mathematik. 1997;75:293-317. doi:10.1007/s002110050240","ieee":"M. Dellnitz and A. Hohmann, “A subdivision algorithm for the computation of unstable manifolds and global attractors,” Numerische Mathematik, vol. 75, pp. 293–317, 1997.","short":"M. Dellnitz, A. Hohmann, Numerische Mathematik 75 (1997) 293–317."},"page":"293-317","user_id":"32643","title":"A subdivision algorithm for the computation of unstable manifolds and global attractors","status":"public","date_created":"2020-05-19T09:07:27Z","publication_identifier":{"issn":["0029-599X","0945-3245"]},"volume":75,"publication_status":"published","author":[{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"},{"first_name":"Andreas","full_name":"Hohmann, Andreas","last_name":"Hohmann"}],"department":[{"_id":"101"}],"publication":"Numerische Mathematik"},{"title":"A Survey of Methods for Computing (un)stable Manifolds of Vector Fields","user_id":"15701","abstract":[{"text":" The computation of global invariant manifolds has seen renewed interest in recent years. We survey different approaches for computing a global stable or unstable manifold of a vector field, where we concentrate on the case of a two-dimensional manifold. All methods are illustrated with the same example — the two-dimensional stable manifold of the origin in the Lorenz system. ","lang":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0218-1274","1793-6551"]},"date_created":"2020-04-16T08:21:52Z","status":"public","department":[{"_id":"101"}],"publication":"International Journal of Bifurcation and Chaos","author":[{"last_name":"Krauskopf","full_name":"Krauskopf, B.","first_name":"B."},{"last_name":"Osinga","full_name":"Osinga, H. M.","first_name":"H. M."},{"full_name":"Doedel, E. J.","first_name":"E. J.","last_name":"Doedel"},{"last_name":"Henderson","first_name":"M. E.","full_name":"Henderson, M. E."},{"last_name":"Guckenheimer","full_name":"Guckenheimer, J.","first_name":"J."},{"full_name":"Vladimirsky, A.","first_name":"A.","last_name":"Vladimirsky"},{"first_name":"M.","full_name":"Dellnitz, M.","last_name":"Dellnitz"},{"full_name":"Junge, O.","first_name":"O.","last_name":"Junge"}],"doi":"10.1142/s0218127405012533","_id":"16627","date_updated":"2022-01-06T06:52:53Z","page":"763-791","type":"journal_article","citation":{"ama":"Krauskopf B, Osinga HM, Doedel EJ, et al. A Survey of Methods for Computing (un)stable Manifolds of Vector Fields. International Journal of Bifurcation and Chaos. 2005:763-791. doi:10.1142/s0218127405012533","apa":"Krauskopf, B., Osinga, H. M., Doedel, E. J., Henderson, M. E., Guckenheimer, J., Vladimirsky, A., … Junge, O. (2005). A Survey of Methods for Computing (un)stable Manifolds of Vector Fields. International Journal of Bifurcation and Chaos, 763–791. https://doi.org/10.1142/s0218127405012533","chicago":"Krauskopf, B., H. M. Osinga, E. J. Doedel, M. E. Henderson, J. Guckenheimer, A. Vladimirsky, M. Dellnitz, and O. Junge. “A Survey of Methods for Computing (Un)Stable Manifolds of Vector Fields.” International Journal of Bifurcation and Chaos, 2005, 763–91. https://doi.org/10.1142/s0218127405012533.","mla":"Krauskopf, B., et al. “A Survey of Methods for Computing (Un)Stable Manifolds of Vector Fields.” International Journal of Bifurcation and Chaos, 2005, pp. 763–91, doi:10.1142/s0218127405012533.","bibtex":"@article{Krauskopf_Osinga_Doedel_Henderson_Guckenheimer_Vladimirsky_Dellnitz_Junge_2005, title={A Survey of Methods for Computing (un)stable Manifolds of Vector Fields}, DOI={10.1142/s0218127405012533}, journal={International Journal of Bifurcation and Chaos}, author={Krauskopf, B. and Osinga, H. M. and Doedel, E. J. and Henderson, M. E. and Guckenheimer, J. and Vladimirsky, A. and Dellnitz, M. and Junge, O.}, year={2005}, pages={763–791} }","short":"B. Krauskopf, H.M. Osinga, E.J. Doedel, M.E. Henderson, J. Guckenheimer, A. Vladimirsky, M. Dellnitz, O. Junge, International Journal of Bifurcation and Chaos (2005) 763–791.","ieee":"B. Krauskopf et al., “A Survey of Methods for Computing (un)stable Manifolds of Vector Fields,” International Journal of Bifurcation and Chaos, pp. 763–791, 2005."},"year":"2005","language":[{"iso":"eng"}]},{"abstract":[{"lang":"eng","text":"Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control, which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort."}],"article_type":"review","user_id":"47427","publication":"Mathematical and Computational Applications","author":[{"last_name":"Peitz","id":"47427","first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"date_created":"2019-03-29T13:27:51Z","status":"public","volume":23,"intvolume":" 23","_id":"8751","issue":"2","main_file_link":[{"url":"https://www.mdpi.com/2297-8747/23/2/30/pdf","open_access":"1"}],"type":"journal_article","year":"2018","citation":{"mla":"Peitz, Sebastian, and Michael Dellnitz. “A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction.” Mathematical and Computational Applications, vol. 23, no. 2, 2018, doi:10.3390/mca23020030.","bibtex":"@article{Peitz_Dellnitz_2018, title={A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction}, volume={23}, DOI={10.3390/mca23020030}, number={2}, journal={Mathematical and Computational Applications}, author={Peitz, Sebastian and Dellnitz, Michael}, year={2018} }","chicago":"Peitz, Sebastian, and Michael Dellnitz. “A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction.” Mathematical and Computational Applications 23, no. 2 (2018). https://doi.org/10.3390/mca23020030.","ama":"Peitz S, Dellnitz M. A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction. Mathematical and Computational Applications. 2018;23(2). doi:10.3390/mca23020030","apa":"Peitz, S., & Dellnitz, M. (2018). A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction. Mathematical and Computational Applications, 23(2). https://doi.org/10.3390/mca23020030","ieee":"S. Peitz and M. Dellnitz, “A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction,” Mathematical and Computational Applications, vol. 23, no. 2, 2018.","short":"S. Peitz, M. Dellnitz, Mathematical and Computational Applications 23 (2018)."},"title":"A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction","department":[{"_id":"101"}],"publication_identifier":{"issn":["2297-8747"]},"publication_status":"published","date_updated":"2022-01-06T07:04:00Z","oa":"1","doi":"10.3390/mca23020030","language":[{"iso":"eng"}]},{"doi":"10.1007/s10898-012-9972-6","date_updated":"2022-01-06T06:52:54Z","_id":"16677","language":[{"iso":"eng"}],"page":"331-345","citation":{"chicago":"Witting, Katrin, Sina Ober-Blöbaum, and Michael Dellnitz. “A Variational Approach to Define Robustness for Parametric Multiobjective Optimization Problems.” Journal of Global Optimization, 2013, 331–45. https://doi.org/10.1007/s10898-012-9972-6.","apa":"Witting, K., Ober-Blöbaum, S., & Dellnitz, M. (2013). A variational approach to define robustness for parametric multiobjective optimization problems. Journal of Global Optimization, 331–345. https://doi.org/10.1007/s10898-012-9972-6","ama":"Witting K, Ober-Blöbaum S, Dellnitz M. A variational approach to define robustness for parametric multiobjective optimization problems. Journal of Global Optimization. 2013:331-345. doi:10.1007/s10898-012-9972-6","bibtex":"@article{Witting_Ober-Blöbaum_Dellnitz_2013, title={A variational approach to define robustness for parametric multiobjective optimization problems}, DOI={10.1007/s10898-012-9972-6}, journal={Journal of Global Optimization}, author={Witting, Katrin and Ober-Blöbaum, Sina and Dellnitz, Michael}, year={2013}, pages={331–345} }","mla":"Witting, Katrin, et al. “A Variational Approach to Define Robustness for Parametric Multiobjective Optimization Problems.” Journal of Global Optimization, 2013, pp. 331–45, doi:10.1007/s10898-012-9972-6.","short":"K. Witting, S. Ober-Blöbaum, M. Dellnitz, Journal of Global Optimization (2013) 331–345.","ieee":"K. Witting, S. Ober-Blöbaum, and M. Dellnitz, “A variational approach to define robustness for parametric multiobjective optimization problems,” Journal of Global Optimization, pp. 331–345, 2013."},"type":"journal_article","year":"2013","user_id":"15701","title":"A variational approach to define robustness for parametric multiobjective optimization problems","date_created":"2020-04-16T10:14:04Z","status":"public","publication_identifier":{"issn":["0925-5001","1573-2916"]},"publication_status":"published","department":[{"_id":"101"}],"publication":"Journal of Global Optimization","author":[{"first_name":"Katrin","full_name":"Witting, Katrin","last_name":"Witting"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"}]},{"extern":"1","user_id":"81513","title":"A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems","department":[{"_id":"101"}],"publication":"Multiscale Modeling & Simulation","author":[{"last_name":"Noé","first_name":"Frank","full_name":"Noé, Frank"},{"first_name":"Feliks","full_name":"Nüske, Feliks","orcid":"0000-0003-2444-7889","last_name":"Nüske","id":"81513"}],"date_created":"2021-04-30T16:51:37Z","status":"public","publication_status":"published","publication_identifier":{"issn":["1540-3459","1540-3467"]},"_id":"21935","date_updated":"2022-01-06T06:55:20Z","doi":"10.1137/110858616","language":[{"iso":"eng"}],"page":"635-655","year":"2013","type":"journal_article","citation":{"apa":"Noé, F., & Nüske, F. (2013). A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems. Multiscale Modeling & Simulation, 635–655. https://doi.org/10.1137/110858616","ama":"Noé F, Nüske F. A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems. Multiscale Modeling & Simulation. 2013:635-655. doi:10.1137/110858616","chicago":"Noé, Frank, and Feliks Nüske. “A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems.” Multiscale Modeling & Simulation, 2013, 635–55. https://doi.org/10.1137/110858616.","mla":"Noé, Frank, and Feliks Nüske. “A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems.” Multiscale Modeling & Simulation, 2013, pp. 635–55, doi:10.1137/110858616.","bibtex":"@article{Noé_Nüske_2013, title={A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems}, DOI={10.1137/110858616}, journal={Multiscale Modeling & Simulation}, author={Noé, Frank and Nüske, Feliks}, year={2013}, pages={635–655} }","short":"F. Noé, F. Nüske, Multiscale Modeling & Simulation (2013) 635–655.","ieee":"F. Noé and F. Nüske, “A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems,” Multiscale Modeling & Simulation, pp. 635–655, 2013."}},{"doi":"10.1088/0951-7715/8/6/009","_id":"16532","date_updated":"2022-01-06T06:52:52Z","language":[{"iso":"eng"}],"citation":{"ieee":"M. Dellnitz and C. Heinrich, “Admissible symmetry increasing bifurcations,” Nonlinearity, pp. 1039–1066, 1995.","short":"M. Dellnitz, C. Heinrich, Nonlinearity (1995) 1039–1066.","bibtex":"@article{Dellnitz_Heinrich_1995, title={Admissible symmetry increasing bifurcations}, DOI={10.1088/0951-7715/8/6/009}, journal={Nonlinearity}, author={Dellnitz, M and Heinrich, C}, year={1995}, pages={1039–1066} }","mla":"Dellnitz, M., and C. Heinrich. “Admissible Symmetry Increasing Bifurcations.” Nonlinearity, 1995, pp. 1039–66, doi:10.1088/0951-7715/8/6/009.","ama":"Dellnitz M, Heinrich C. Admissible symmetry increasing bifurcations. Nonlinearity. 1995:1039-1066. doi:10.1088/0951-7715/8/6/009","apa":"Dellnitz, M., & Heinrich, C. (1995). Admissible symmetry increasing bifurcations. Nonlinearity, 1039–1066. https://doi.org/10.1088/0951-7715/8/6/009","chicago":"Dellnitz, M, and C Heinrich. “Admissible Symmetry Increasing Bifurcations.” Nonlinearity, 1995, 1039–66. https://doi.org/10.1088/0951-7715/8/6/009."},"type":"journal_article","year":"1995","page":"1039-1066","user_id":"15701","title":"Admissible symmetry increasing bifurcations","status":"public","date_created":"2020-04-15T08:25:12Z","publication_identifier":{"issn":["0951-7715","1361-6544"]},"publication_status":"published","author":[{"last_name":"Dellnitz","full_name":"Dellnitz, M","first_name":"M"},{"last_name":"Heinrich","first_name":"C","full_name":"Heinrich, C"}],"department":[{"_id":"101"}],"publication":"Nonlinearity"},{"user_id":"47427","title":"Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control","date_created":"2020-04-16T14:08:51Z","status":"public","publication_status":"published","publication_identifier":{"issn":["0306-4522"]},"publication":"Neuroscience","department":[{"_id":"101"}],"author":[{"full_name":"Vieluf, Solveig","first_name":"Solveig","last_name":"Vieluf"},{"last_name":"Mora","first_name":"Karin","full_name":"Mora, Karin"},{"last_name":"Gölz","full_name":"Gölz, Christian","first_name":"Christian"},{"last_name":"Reuter","first_name":"Eva-Maria","full_name":"Reuter, Eva-Maria"},{"last_name":"Godde","full_name":"Godde, Ben","first_name":"Ben"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"full_name":"Reinsberger, Claus","first_name":"Claus","last_name":"Reinsberger"},{"full_name":"Voelcker-Rehage, Claudia","first_name":"Claudia","last_name":"Voelcker-Rehage"}],"doi":"10.1016/j.neuroscience.2018.07.025","date_updated":"2022-01-06T06:52:55Z","_id":"16714","language":[{"iso":"eng"}],"page":"203-213","citation":{"ama":"Vieluf S, Mora K, Gölz C, et al. Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control. Neuroscience. 2018:203-213. doi:10.1016/j.neuroscience.2018.07.025","apa":"Vieluf, S., Mora, K., Gölz, C., Reuter, E.-M., Godde, B., Dellnitz, M., … Voelcker-Rehage, C. (2018). Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control. Neuroscience, 203–213. https://doi.org/10.1016/j.neuroscience.2018.07.025","chicago":"Vieluf, Solveig, Karin Mora, Christian Gölz, Eva-Maria Reuter, Ben Godde, Michael Dellnitz, Claus Reinsberger, and Claudia Voelcker-Rehage. “Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control.” Neuroscience, 2018, 203–13. https://doi.org/10.1016/j.neuroscience.2018.07.025.","bibtex":"@article{Vieluf_Mora_Gölz_Reuter_Godde_Dellnitz_Reinsberger_Voelcker-Rehage_2018, title={Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control}, DOI={10.1016/j.neuroscience.2018.07.025}, journal={Neuroscience}, author={Vieluf, Solveig and Mora, Karin and Gölz, Christian and Reuter, Eva-Maria and Godde, Ben and Dellnitz, Michael and Reinsberger, Claus and Voelcker-Rehage, Claudia}, year={2018}, pages={203–213} }","mla":"Vieluf, Solveig, et al. “Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control.” Neuroscience, 2018, pp. 203–13, doi:10.1016/j.neuroscience.2018.07.025.","short":"S. Vieluf, K. Mora, C. Gölz, E.-M. Reuter, B. Godde, M. Dellnitz, C. Reinsberger, C. Voelcker-Rehage, Neuroscience (2018) 203–213.","ieee":"S. Vieluf et al., “Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control,” Neuroscience, pp. 203–213, 2018."},"year":"2018","type":"journal_article"},{"year":"1997","citation":{"ieee":"M. Dellnitz and O. Junge, “Almost Invariant Sets in Chua’s Circuit,” International Journal of Bifurcation and Chaos, pp. 2475–2485, 1997.","short":"M. Dellnitz, O. Junge, International Journal of Bifurcation and Chaos (1997) 2475–2485.","mla":"Dellnitz, Michael, and Oliver Junge. “Almost Invariant Sets in Chua’s Circuit.” International Journal of Bifurcation and Chaos, 1997, pp. 2475–85, doi:10.1142/s0218127497001655.","bibtex":"@article{Dellnitz_Junge_1997, title={Almost Invariant Sets in Chua’s Circuit}, DOI={10.1142/s0218127497001655}, journal={International Journal of Bifurcation and Chaos}, author={Dellnitz, Michael and Junge, Oliver}, year={1997}, pages={2475–2485} }","apa":"Dellnitz, M., & Junge, O. (1997). Almost Invariant Sets in Chua’s Circuit. International Journal of Bifurcation and Chaos, 2475–2485. https://doi.org/10.1142/s0218127497001655","ama":"Dellnitz M, Junge O. Almost Invariant Sets in Chua’s Circuit. International Journal of Bifurcation and Chaos. 1997:2475-2485. doi:10.1142/s0218127497001655","chicago":"Dellnitz, Michael, and Oliver Junge. “Almost Invariant Sets in Chua’s Circuit.” International Journal of Bifurcation and Chaos, 1997, 2475–85. https://doi.org/10.1142/s0218127497001655."},"type":"journal_article","page":"2475-2485","language":[{"iso":"eng"}],"date_updated":"2022-01-06T06:52:52Z","_id":"16535","doi":"10.1142/s0218127497001655","author":[{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"full_name":"Junge, Oliver","first_name":"Oliver","last_name":"Junge"}],"publication":"International Journal of Bifurcation and Chaos","department":[{"_id":"101"}],"publication_status":"published","publication_identifier":{"issn":["0218-1274","1793-6551"]},"status":"public","date_created":"2020-04-15T08:31:50Z","abstract":[{"text":" Recently multilevel subdivision techniques have been introduced in the numerical investigation of complicated dynamical behavior. We illustrate the applicability and efficiency of these methods by a detailed numerical study of Chua's circuit. In particular we will show that there exist two regions in phase space which are almost invariant in the sense that typical trajectories stay inside each of these sets on average for quite a long time. ","lang":"eng"}],"title":"Almost Invariant Sets in Chua's Circuit","user_id":"15701"},{"_id":"16614","date_updated":"2022-01-06T06:52:53Z","doi":"10.1016/s0960-0779(96)00118-x","page":"525-534","type":"journal_article","citation":{"short":"R. Guder, M. Dellnitz, E. Kreuzer, Chaos, Solitons & Fractals (1997) 525–534.","ieee":"R. Guder, M. Dellnitz, and E. Kreuzer, “An adaptive method for the approximation of the generalized cell mapping,” Chaos, Solitons & Fractals, pp. 525–534, 1997.","chicago":"Guder, Rabbijah, Michael Dellnitz, and Edwin Kreuzer. “An Adaptive Method for the Approximation of the Generalized Cell Mapping.” Chaos, Solitons & Fractals, 1997, 525–34. https://doi.org/10.1016/s0960-0779(96)00118-x.","ama":"Guder R, Dellnitz M, Kreuzer E. An adaptive method for the approximation of the generalized cell mapping. Chaos, Solitons & Fractals. 1997:525-534. doi:10.1016/s0960-0779(96)00118-x","apa":"Guder, R., Dellnitz, M., & Kreuzer, E. (1997). An adaptive method for the approximation of the generalized cell mapping. Chaos, Solitons & Fractals, 525–534. https://doi.org/10.1016/s0960-0779(96)00118-x","mla":"Guder, Rabbijah, et al. “An Adaptive Method for the Approximation of the Generalized Cell Mapping.” Chaos, Solitons & Fractals, 1997, pp. 525–34, doi:10.1016/s0960-0779(96)00118-x.","bibtex":"@article{Guder_Dellnitz_Kreuzer_1997, title={An adaptive method for the approximation of the generalized cell mapping}, DOI={10.1016/s0960-0779(96)00118-x}, journal={Chaos, Solitons & Fractals}, author={Guder, Rabbijah and Dellnitz, Michael and Kreuzer, Edwin}, year={1997}, pages={525–534} }"},"year":"1997","language":[{"iso":"eng"}],"title":"An adaptive method for the approximation of the generalized cell mapping","user_id":"15701","department":[{"_id":"101"}],"publication":"Chaos, Solitons & Fractals","author":[{"full_name":"Guder, Rabbijah","first_name":"Rabbijah","last_name":"Guder"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"full_name":"Kreuzer, Edwin","first_name":"Edwin","last_name":"Kreuzer"}],"publication_identifier":{"issn":["0960-0779"]},"publication_status":"published","date_created":"2020-04-16T08:05:37Z","status":"public"},{"author":[{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"},{"last_name":"Junge","full_name":"Junge, Oliver","first_name":"Oliver"}],"department":[{"_id":"101"}],"publication":"Computing and Visualization in Science","publication_status":"published","publication_identifier":{"issn":["1432-9360","1433-0369"]},"status":"public","date_created":"2020-04-15T08:33:03Z","title":"An adaptive subdivision technique for the approximation of attractors and invariant measures","user_id":"15701","type":"journal_article","citation":{"bibtex":"@article{Dellnitz_Junge_1998, title={An adaptive subdivision technique for the approximation of attractors and invariant measures}, DOI={10.1007/s007910050006}, journal={Computing and Visualization in Science}, author={Dellnitz, Michael and Junge, Oliver}, year={1998}, pages={63–68} }","mla":"Dellnitz, Michael, and Oliver Junge. “An Adaptive Subdivision Technique for the Approximation of Attractors and Invariant Measures.” Computing and Visualization in Science, 1998, pp. 63–68, doi:10.1007/s007910050006.","ama":"Dellnitz M, Junge O. An adaptive subdivision technique for the approximation of attractors and invariant measures. Computing and Visualization in Science. 1998:63-68. doi:10.1007/s007910050006","apa":"Dellnitz, M., & Junge, O. (1998). An adaptive subdivision technique for the approximation of attractors and invariant measures. Computing and Visualization in Science, 63–68. https://doi.org/10.1007/s007910050006","chicago":"Dellnitz, Michael, and Oliver Junge. “An Adaptive Subdivision Technique for the Approximation of Attractors and Invariant Measures.” Computing and Visualization in Science, 1998, 63–68. https://doi.org/10.1007/s007910050006.","ieee":"M. Dellnitz and O. Junge, “An adaptive subdivision technique for the approximation of attractors and invariant measures,” Computing and Visualization in Science, pp. 63–68, 1998.","short":"M. Dellnitz, O. Junge, Computing and Visualization in Science (1998) 63–68."},"year":"1998","page":"63-68","language":[{"iso":"eng"}],"date_updated":"2022-01-06T06:52:52Z","_id":"16536","doi":"10.1007/s007910050006"},{"page":"213-222","type":"journal_article","citation":{"ieee":"O. Junge, “An adaptive subdivision technique for the approximation of attractors and invariant measures: proof of convergence,” Dynamical Systems, pp. 213–222, 2001.","short":"O. Junge, Dynamical Systems (2001) 213–222.","bibtex":"@article{Junge_2001, title={An adaptive subdivision technique for the approximation of attractors and invariant measures: proof of convergence}, DOI={10.1080/14689360109696233}, journal={Dynamical Systems}, author={Junge, Oliver}, year={2001}, pages={213–222} }","mla":"Junge, Oliver. “An Adaptive Subdivision Technique for the Approximation of Attractors and Invariant Measures: Proof of Convergence.” Dynamical Systems, 2001, pp. 213–22, doi:10.1080/14689360109696233.","ama":"Junge O. An adaptive subdivision technique for the approximation of attractors and invariant measures: proof of convergence. Dynamical Systems. 2001:213-222. doi:10.1080/14689360109696233","apa":"Junge, O. (2001). An adaptive subdivision technique for the approximation of attractors and invariant measures: proof of convergence. Dynamical Systems, 213–222. https://doi.org/10.1080/14689360109696233","chicago":"Junge, Oliver. “An Adaptive Subdivision Technique for the Approximation of Attractors and Invariant Measures: Proof of Convergence.” Dynamical Systems, 2001, 213–22. https://doi.org/10.1080/14689360109696233."},"year":"2001","language":[{"iso":"eng"}],"doi":"10.1080/14689360109696233","date_updated":"2022-01-06T06:52:53Z","_id":"16617","publication_status":"published","publication_identifier":{"issn":["1468-9367","1468-9375"]},"date_created":"2020-04-16T08:09:10Z","status":"public","department":[{"_id":"101"}],"publication":"Dynamical Systems","author":[{"last_name":"Junge","first_name":"Oliver","full_name":"Junge, Oliver"}],"title":"An adaptive subdivision technique for the approximation of attractors and invariant measures: proof of convergence","user_id":"15701"},{"date_updated":"2022-01-06T06:52:53Z","_id":"16624","doi":"10.1016/j.cam.2010.12.026","citation":{"ieee":"S. Klus, T. Sahai, C. Liu, and M. Dellnitz, “An efficient algorithm for the parallel solution of high-dimensional differential equations,” Journal of Computational and Applied Mathematics, pp. 3053–3062, 2011.","short":"S. Klus, T. Sahai, C. Liu, M. Dellnitz, Journal of Computational and Applied Mathematics (2011) 3053–3062.","mla":"Klus, Stefan, et al. “An Efficient Algorithm for the Parallel Solution of High-Dimensional Differential Equations.” Journal of Computational and Applied Mathematics, 2011, pp. 3053–62, doi:10.1016/j.cam.2010.12.026.","bibtex":"@article{Klus_Sahai_Liu_Dellnitz_2011, title={An efficient algorithm for the parallel solution of high-dimensional differential equations}, DOI={10.1016/j.cam.2010.12.026}, journal={Journal of Computational and Applied Mathematics}, author={Klus, Stefan and Sahai, Tuhin and Liu, Cong and Dellnitz, Michael}, year={2011}, pages={3053–3062} }","chicago":"Klus, Stefan, Tuhin Sahai, Cong Liu, and Michael Dellnitz. “An Efficient Algorithm for the Parallel Solution of High-Dimensional Differential Equations.” Journal of Computational and Applied Mathematics, 2011, 3053–62. https://doi.org/10.1016/j.cam.2010.12.026.","apa":"Klus, S., Sahai, T., Liu, C., & Dellnitz, M. (2011). An efficient algorithm for the parallel solution of high-dimensional differential equations. Journal of Computational and Applied Mathematics, 3053–3062. https://doi.org/10.1016/j.cam.2010.12.026","ama":"Klus S, Sahai T, Liu C, Dellnitz M. An efficient algorithm for the parallel solution of high-dimensional differential equations. Journal of Computational and Applied Mathematics. 2011:3053-3062. doi:10.1016/j.cam.2010.12.026"},"type":"journal_article","year":"2011","page":"3053-3062","language":[{"iso":"eng"}],"title":"An efficient algorithm for the parallel solution of high-dimensional differential equations","user_id":"15701","author":[{"first_name":"Stefan","full_name":"Klus, Stefan","last_name":"Klus"},{"first_name":"Tuhin","full_name":"Sahai, Tuhin","last_name":"Sahai"},{"full_name":"Liu, Cong","first_name":"Cong","last_name":"Liu"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"publication":"Journal of Computational and Applied Mathematics","department":[{"_id":"101"}],"publication_status":"published","publication_identifier":{"issn":["0377-0427"]},"status":"public","date_created":"2020-04-16T08:18:33Z"},{"doi":"10.1007/s10957-020-01803-w","oa":"1","date_updated":"2022-01-06T06:52:57Z","language":[{"iso":"eng"}],"title":"An efficient descent method for locally Lipschitz multiobjective optimization problems","publication_status":"published","department":[{"_id":"101"}],"_id":"16867","intvolume":" 188","type":"journal_article","citation":{"mla":"Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems.” Journal of Optimization Theory and Applications, vol. 188, 2021, pp. 696–723, doi:10.1007/s10957-020-01803-w.","bibtex":"@article{Gebken_Peitz_2021, title={An efficient descent method for locally Lipschitz multiobjective optimization problems}, volume={188}, DOI={10.1007/s10957-020-01803-w}, journal={Journal of Optimization Theory and Applications}, author={Gebken, Bennet and Peitz, Sebastian}, year={2021}, pages={696–723} }","ama":"Gebken B, Peitz S. An efficient descent method for locally Lipschitz multiobjective optimization problems. Journal of Optimization Theory and Applications. 2021;188:696-723. doi:10.1007/s10957-020-01803-w","apa":"Gebken, B., & Peitz, S. (2021). An efficient descent method for locally Lipschitz multiobjective optimization problems. Journal of Optimization Theory and Applications, 188, 696–723. https://doi.org/10.1007/s10957-020-01803-w","chicago":"Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems.” Journal of Optimization Theory and Applications 188 (2021): 696–723. https://doi.org/10.1007/s10957-020-01803-w.","ieee":"B. Gebken and S. Peitz, “An efficient descent method for locally Lipschitz multiobjective optimization problems,” Journal of Optimization Theory and Applications, vol. 188, pp. 696–723, 2021.","short":"B. Gebken, S. Peitz, Journal of Optimization Theory and Applications 188 (2021) 696–723."},"year":"2021","page":"696-723","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10957-020-01803-w.pdf","open_access":"1"}],"user_id":"47427","abstract":[{"text":"In this article, we present an efficient descent method for locally Lipschitz\r\ncontinuous multiobjective optimization problems (MOPs). The method is realized\r\nby combining a theoretical result regarding the computation of descent\r\ndirections for nonsmooth MOPs with a practical method to approximate the\r\nsubdifferentials of the objective functions. We show convergence to points\r\nwhich satisfy a necessary condition for Pareto optimality. Using a set of test\r\nproblems, we compare our method to the multiobjective proximal bundle method by\r\nM\\\"akel\\\"a. The results indicate that our method is competitive while being\r\neasier to implement. While the number of objective function evaluations is\r\nlarger, the overall number of subgradient evaluations is lower. Finally, we\r\nshow that our method can be combined with a subdivision algorithm to compute\r\nentire Pareto sets of nonsmooth MOPs.","lang":"eng"}],"volume":188,"status":"public","date_created":"2020-04-27T09:11:22Z","author":[{"id":"32643","last_name":"Gebken","full_name":"Gebken, Bennet","first_name":"Bennet"},{"id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian"}],"publication":"Journal of Optimization Theory and Applications"},{"user_id":"47427","title":"Analysis of team and player performance using recorded trajectory data","department":[{"_id":"101"}],"publication":"Performance Analysis of Sport IX, Part 8, Routledge","author":[{"last_name":"Timmermann","first_name":"Robert","full_name":"Timmermann, Robert"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"date_created":"2020-05-20T08:42:19Z","status":"public","date_updated":"2022-01-06T06:53:03Z","_id":"17048","language":[{"iso":"eng"}],"type":"conference","year":"2013","citation":{"ama":"Timmermann R, Dellnitz M. Analysis of team and player performance using recorded trajectory data. In: Performance Analysis of Sport IX, Part 8, Routledge. ; 2013.","apa":"Timmermann, R., & Dellnitz, M. (2013). Analysis of team and player performance using recorded trajectory data. In Performance Analysis of Sport IX, Part 8, Routledge.","chicago":"Timmermann, Robert, and Michael Dellnitz. “Analysis of Team and Player Performance Using Recorded Trajectory Data.” In Performance Analysis of Sport IX, Part 8, Routledge, 2013.","bibtex":"@inproceedings{Timmermann_Dellnitz_2013, title={Analysis of team and player performance using recorded trajectory data}, booktitle={Performance Analysis of Sport IX, Part 8, Routledge}, author={Timmermann, Robert and Dellnitz, Michael}, year={2013} }","mla":"Timmermann, Robert, and Michael Dellnitz. “Analysis of Team and Player Performance Using Recorded Trajectory Data.” Performance Analysis of Sport IX, Part 8, Routledge, 2013.","short":"R. Timmermann, M. Dellnitz, in: Performance Analysis of Sport IX, Part 8, Routledge, 2013.","ieee":"R. Timmermann and M. Dellnitz, “Analysis of team and player performance using recorded trajectory data,” in Performance Analysis of Sport IX, Part 8, Routledge, 2013."}},{"oa":"1","_id":"16293","date_updated":"2022-01-06T06:52:48Z","language":[{"iso":"eng"}],"year":"2018","type":"preprint","citation":{"apa":"Klus, S., Peitz, S., & Schuster, I. (2018). Analyzing high-dimensional time-series data using kernel transfer operator eigenfunctions. ArXiv:1805.10118.","ama":"Klus S, Peitz S, Schuster I. Analyzing high-dimensional time-series data using kernel transfer operator eigenfunctions. arXiv:180510118. 2018.","chicago":"Klus, Stefan, Sebastian Peitz, and Ingmar Schuster. “Analyzing High-Dimensional Time-Series Data Using Kernel Transfer Operator Eigenfunctions.” ArXiv:1805.10118, 2018.","mla":"Klus, Stefan, et al. “Analyzing High-Dimensional Time-Series Data Using Kernel Transfer Operator Eigenfunctions.” ArXiv:1805.10118, 2018.","bibtex":"@article{Klus_Peitz_Schuster_2018, title={Analyzing high-dimensional time-series data using kernel transfer operator eigenfunctions}, journal={arXiv:1805.10118}, author={Klus, Stefan and Peitz, Sebastian and Schuster, Ingmar}, year={2018} }","short":"S. Klus, S. Peitz, I. Schuster, ArXiv:1805.10118 (2018).","ieee":"S. Klus, S. Peitz, and I. Schuster, “Analyzing high-dimensional time-series data using kernel transfer operator eigenfunctions,” arXiv:1805.10118. 2018."},"main_file_link":[{"url":"https://arxiv.org/pdf/1805.10118.pdf","open_access":"1"}],"user_id":"47427","title":"Analyzing high-dimensional time-series data using kernel transfer operator eigenfunctions","abstract":[{"text":"Kernel transfer operators, which can be regarded as approximations of\r\ntransfer operators such as the Perron-Frobenius or Koopman operator in\r\nreproducing kernel Hilbert spaces, are defined in terms of covariance and\r\ncross-covariance operators and have been shown to be closely related to the\r\nconditional mean embedding framework developed by the machine learning\r\ncommunity. The goal of this paper is to show how the dominant eigenfunctions of\r\nthese operators in combination with gradient-based optimization techniques can\r\nbe used to detect long-lived coherent patterns in high-dimensional time-series\r\ndata. The results will be illustrated using video data and a fluid flow\r\nexample.","lang":"eng"}],"project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"date_created":"2020-03-13T12:44:12Z","status":"public","publication":"arXiv:1805.10118","department":[{"_id":"101"}],"author":[{"last_name":"Klus","full_name":"Klus, Stefan","first_name":"Stefan"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","id":"47427"},{"last_name":"Schuster","first_name":"Ingmar","full_name":"Schuster, Ingmar"}]},{"publication_identifier":{"issn":["2154-4573"],"isbn":["9781584885504","9781420010749"]},"publication_status":"published","date_created":"2020-04-16T09:33:00Z","status":"public","publication":"Handbook of Approximation Algorithms and Metaheuristics","department":[{"_id":"101"}],"author":[{"last_name":"Preis","full_name":"Preis, Robert","first_name":"Robert"},{"full_name":"Monien, Burkhard","first_name":"Burkhard","last_name":"Monien"},{"full_name":"Schamberger, Stefan","first_name":"Stefan","last_name":"Schamberger"}],"title":"Approximation Algorithms for Multilevel Graph Partitioning","user_id":"15701","year":"2007","citation":{"apa":"Preis, R., Monien, B., & Schamberger, S. (2007). Approximation Algorithms for Multilevel Graph Partitioning. In Handbook of Approximation Algorithms and Metaheuristics. https://doi.org/10.1201/9781420010749.ch60","ama":"Preis R, Monien B, Schamberger S. Approximation Algorithms for Multilevel Graph Partitioning. In: Handbook of Approximation Algorithms and Metaheuristics. ; 2007. doi:10.1201/9781420010749.ch60","chicago":"Preis, Robert, Burkhard Monien, and Stefan Schamberger. “Approximation Algorithms for Multilevel Graph Partitioning.” In Handbook of Approximation Algorithms and Metaheuristics, 2007. https://doi.org/10.1201/9781420010749.ch60.","mla":"Preis, Robert, et al. “Approximation Algorithms for Multilevel Graph Partitioning.” Handbook of Approximation Algorithms and Metaheuristics, 2007, doi:10.1201/9781420010749.ch60.","bibtex":"@inbook{Preis_Monien_Schamberger_2007, title={Approximation Algorithms for Multilevel Graph Partitioning}, DOI={10.1201/9781420010749.ch60}, booktitle={Handbook of Approximation Algorithms and Metaheuristics}, author={Preis, Robert and Monien, Burkhard and Schamberger, Stefan}, year={2007} }","short":"R. Preis, B. Monien, S. Schamberger, in: Handbook of Approximation Algorithms and Metaheuristics, 2007.","ieee":"R. Preis, B. Monien, and S. Schamberger, “Approximation Algorithms for Multilevel Graph Partitioning,” in Handbook of Approximation Algorithms and Metaheuristics, 2007."},"type":"book_chapter","language":[{"iso":"eng"}],"doi":"10.1201/9781420010749.ch60","date_updated":"2022-01-06T06:52:53Z","_id":"16658"},{"status":"public","date_created":"2020-04-16T05:41:52Z","publication_status":"published","publication_identifier":{"issn":["1617-7061"]},"author":[{"full_name":"Demoures, Francois","first_name":"Francois","last_name":"Demoures"},{"first_name":"Francois","full_name":"Gay-Balmaz, Francois","last_name":"Gay-Balmaz"},{"full_name":"Leitz, Thomas","first_name":"Thomas","last_name":"Leitz"},{"last_name":"Leyendecker","full_name":"Leyendecker, Sigrid","first_name":"Sigrid"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"last_name":"Ratiu","full_name":"Ratiu, Tudor S.","first_name":"Tudor S."}],"department":[{"_id":"101"}],"publication":"PAMM","user_id":"15701","title":"Asynchronous variational Lie group integration for geometrically exact beam dynamics","language":[{"iso":"eng"}],"year":"2013","type":"journal_article","citation":{"apa":"Demoures, F., Gay-Balmaz, F., Leitz, T., Leyendecker, S., Ober-Blöbaum, S., & Ratiu, T. S. (2013). Asynchronous variational Lie group integration for geometrically exact beam dynamics. PAMM, 45–46. https://doi.org/10.1002/pamm.201310018","ama":"Demoures F, Gay-Balmaz F, Leitz T, Leyendecker S, Ober-Blöbaum S, Ratiu TS. Asynchronous variational Lie group integration for geometrically exact beam dynamics. PAMM. 2013:45-46. doi:10.1002/pamm.201310018","chicago":"Demoures, Francois, Francois Gay-Balmaz, Thomas Leitz, Sigrid Leyendecker, Sina Ober-Blöbaum, and Tudor S. Ratiu. “Asynchronous Variational Lie Group Integration for Geometrically Exact Beam Dynamics.” PAMM, 2013, 45–46. https://doi.org/10.1002/pamm.201310018.","mla":"Demoures, Francois, et al. “Asynchronous Variational Lie Group Integration for Geometrically Exact Beam Dynamics.” PAMM, 2013, pp. 45–46, doi:10.1002/pamm.201310018.","bibtex":"@article{Demoures_Gay-Balmaz_Leitz_Leyendecker_Ober-Blöbaum_Ratiu_2013, title={Asynchronous variational Lie group integration for geometrically exact beam dynamics}, DOI={10.1002/pamm.201310018}, journal={PAMM}, author={Demoures, Francois and Gay-Balmaz, Francois and Leitz, Thomas and Leyendecker, Sigrid and Ober-Blöbaum, Sina and Ratiu, Tudor S.}, year={2013}, pages={45–46} }","short":"F. Demoures, F. Gay-Balmaz, T. Leitz, S. Leyendecker, S. Ober-Blöbaum, T.S. Ratiu, PAMM (2013) 45–46.","ieee":"F. Demoures, F. Gay-Balmaz, T. Leitz, S. Leyendecker, S. Ober-Blöbaum, and T. S. Ratiu, “Asynchronous variational Lie group integration for geometrically exact beam dynamics,” PAMM, pp. 45–46, 2013."},"page":"45-46","doi":"10.1002/pamm.201310018","date_updated":"2022-01-06T06:52:52Z","_id":"16583"},{"extern":"1","title":"Coarse-graining molecular systems by spectral matching","user_id":"81513","publication":"The Journal of Chemical Physics","department":[{"_id":"101"}],"author":[{"first_name":"Feliks","full_name":"Nüske, Feliks","orcid":"0000-0003-2444-7889","last_name":"Nüske","id":"81513"},{"last_name":"Boninsegna","full_name":"Boninsegna, Lorenzo","first_name":"Lorenzo"},{"last_name":"Clementi","full_name":"Clementi, Cecilia","first_name":"Cecilia"}],"publication_status":"published","publication_identifier":{"issn":["0021-9606","1089-7690"]},"date_created":"2021-04-30T17:01:13Z","status":"public","_id":"21944","date_updated":"2022-01-06T06:55:20Z","doi":"10.1063/1.5100131","article_number":"044116","citation":{"chicago":"Nüske, Feliks, Lorenzo Boninsegna, and Cecilia Clementi. “Coarse-Graining Molecular Systems by Spectral Matching.” The Journal of Chemical Physics, 2019. https://doi.org/10.1063/1.5100131.","ama":"Nüske F, Boninsegna L, Clementi C. Coarse-graining molecular systems by spectral matching. The Journal of Chemical Physics. 2019. doi:10.1063/1.5100131","apa":"Nüske, F., Boninsegna, L., & Clementi, C. (2019). Coarse-graining molecular systems by spectral matching. The Journal of Chemical Physics. https://doi.org/10.1063/1.5100131","mla":"Nüske, Feliks, et al. “Coarse-Graining Molecular Systems by Spectral Matching.” The Journal of Chemical Physics, 044116, 2019, doi:10.1063/1.5100131.","bibtex":"@article{Nüske_Boninsegna_Clementi_2019, title={Coarse-graining molecular systems by spectral matching}, DOI={10.1063/1.5100131}, number={044116}, journal={The Journal of Chemical Physics}, author={Nüske, Feliks and Boninsegna, Lorenzo and Clementi, Cecilia}, year={2019} }","short":"F. Nüske, L. Boninsegna, C. Clementi, The Journal of Chemical Physics (2019).","ieee":"F. Nüske, L. Boninsegna, and C. Clementi, “Coarse-graining molecular systems by spectral matching,” The Journal of Chemical Physics, 2019."},"year":"2019","type":"journal_article","language":[{"iso":"eng"}]},{"user_id":"32643","title":"Collisions of chaotic attractors","author":[{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"}],"publication":"Schlaglichter der Forschung: Zum 75. Jahrestag der Universität Hamburg","department":[{"_id":"101"}],"status":"public","date_created":"2020-05-19T09:06:20Z","date_updated":"2022-01-06T06:53:02Z","_id":"17014","language":[{"iso":"eng"}],"citation":{"bibtex":"@article{Dellnitz_1994, title={Collisions of chaotic attractors}, journal={Schlaglichter der Forschung: Zum 75. Jahrestag der Universität Hamburg}, author={Dellnitz, Michael}, year={1994}, pages={411–428} }","mla":"Dellnitz, Michael. “Collisions of Chaotic Attractors.” Schlaglichter Der Forschung: Zum 75. Jahrestag Der Universität Hamburg, 1994, pp. 411–28.","ama":"Dellnitz M. Collisions of chaotic attractors. Schlaglichter der Forschung: Zum 75 Jahrestag der Universität Hamburg. 1994:411-428.","apa":"Dellnitz, M. (1994). Collisions of chaotic attractors. Schlaglichter Der Forschung: Zum 75. Jahrestag Der Universität Hamburg, 411–428.","chicago":"Dellnitz, Michael. “Collisions of Chaotic Attractors.” Schlaglichter Der Forschung: Zum 75. Jahrestag Der Universität Hamburg, 1994, 411–28.","ieee":"M. Dellnitz, “Collisions of chaotic attractors,” Schlaglichter der Forschung: Zum 75. Jahrestag der Universität Hamburg, pp. 411–428, 1994.","short":"M. Dellnitz, Schlaglichter Der Forschung: Zum 75. Jahrestag Der Universität Hamburg (1994) 411–428."},"type":"journal_article","year":"1994","page":"411-428"},{"main_file_link":[{"open_access":"1","url":"https://digital.ub.uni-paderborn.de/hs/download/pdf/6531779"}],"type":"dissertation","year":"2022","citation":{"ieee":"B. Gebken, Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization. 2022.","short":"B. Gebken, Computation and Analysis of Pareto Critical Sets in Smooth and Nonsmooth Multiobjective Optimization, 2022.","mla":"Gebken, Bennet. Computation and Analysis of Pareto Critical Sets in Smooth and Nonsmooth Multiobjective Optimization. 2022, doi:10.17619/UNIPB/1-1327.","bibtex":"@book{Gebken_2022, title={Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization}, DOI={10.17619/UNIPB/1-1327}, author={Gebken, Bennet}, year={2022} }","ama":"Gebken B. Computation and Analysis of Pareto Critical Sets in Smooth and Nonsmooth Multiobjective Optimization.; 2022. doi:10.17619/UNIPB/1-1327","apa":"Gebken, B. (2022). Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization. https://doi.org/10.17619/UNIPB/1-1327","chicago":"Gebken, Bennet. Computation and Analysis of Pareto Critical Sets in Smooth and Nonsmooth Multiobjective Optimization, 2022. https://doi.org/10.17619/UNIPB/1-1327."},"language":[{"iso":"eng"}],"supervisor":[{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"}],"date_updated":"2022-06-01T07:13:09Z","_id":"31556","doi":"10.17619/UNIPB/1-1327","oa":"1","department":[{"_id":"101"}],"author":[{"last_name":"Gebken","id":"32643","first_name":"Bennet","full_name":"Gebken, Bennet"}],"date_created":"2022-06-01T06:48:08Z","status":"public","abstract":[{"text":"Mehrzieloptimierung behandelt Probleme, bei denen mehrere skalare Zielfunktionen simultan optimiert werden sollen. Ein Punkt ist in diesem Fall optimal, wenn es keinen anderen Punkt gibt, der mindestens genauso gut ist in allen Zielfunktionen und besser in mindestens einer Zielfunktion. Ein notwendiges Optimalitätskriterium lässt sich über Ableitungsinformationen erster Ordnung der Zielfunktionen herleiten. Die Menge der Punkte, die dieses notwendige Kriterium erfüllen, wird als Pareto-kritische Menge bezeichnet. Diese Arbeit enthält neue Resultate über Pareto-kritische Mengen für glatte und nicht-glatte Mehrzieloptimierungsprobleme, sowohl was deren Berechnung betrifft als auch deren Struktur. Im glatten Fall erfolgt die Berechnung über ein Fortsetzungsverfahren, im nichtglatten Fall über ein Abstiegsverfahren. Anschließend wird die Struktur des Randes der Pareto-kritischen Menge analysiert, welcher aus Pareto-kritischen Mengen kleinerer Subprobleme besteht. Schlussendlich werden inverse Probleme betrachtet, bei denen zu einer gegebenen Datenmenge ein Zielfunktionsvektor gefunden werden soll, für den die Datenpunkte kritisch sind.","lang":"ger"},{"lang":"eng","text":"Multiobjective optimization is concerned with the simultaneous optimization of multiple scalar-valued functions. In this case, a point is optimal if there is no other point that is at least as good in all objectives and better in at least one objective. A necessary condition for optimality can be derived based on first-order information of the objectives. The set of points that satisfy this necessary condition is called the Pareto critical set. This thesis presents new results about Pareto critical sets for smooth and nonsmooth multiobjective optimization problems, both in terms of their efficient computation and structural properties. In the smooth case they are computed via a continuation method and in the nonsmooth case via a descent method. Afterwards, the structure of the boundary of the Pareto critical set is analyzed, which consists of Pareto critical sets of smaller subproblems. Finally, inverse problems are considered, where a data set is given and an objective vector is sought for which the data points are critical."}],"title":"Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization","user_id":"32643"},{"place":"Berlin, Heidelberg","user_id":"15701","title":"Computation of Essential Molecular Dynamics by Subdivision Techniques","publication":"Computational Molecular Dynamics: Challenges, Methods, Ideas","department":[{"_id":"101"}],"author":[{"first_name":"Peter","full_name":"Deuflhard, Peter","last_name":"Deuflhard"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"last_name":"Junge","first_name":"Oliver","full_name":"Junge, Oliver"},{"first_name":"Christof","full_name":"Schütte, Christof","last_name":"Schütte"}],"date_created":"2020-04-16T05:43:16Z","status":"public","publication_status":"published","publication_identifier":{"issn":["1439-7358"],"isbn":["9783540632429","9783642583605"]},"_id":"16584","date_updated":"2022-01-06T06:52:52Z","doi":"10.1007/978-3-642-58360-5_5","language":[{"iso":"eng"}],"year":"1999","citation":{"ieee":"P. Deuflhard, M. Dellnitz, O. Junge, and C. Schütte, “Computation of Essential Molecular Dynamics by Subdivision Techniques,” in Computational Molecular Dynamics: Challenges, Methods, Ideas, Berlin, Heidelberg, 1999.","short":"P. Deuflhard, M. Dellnitz, O. Junge, C. Schütte, in: Computational Molecular Dynamics: Challenges, Methods, Ideas, Berlin, Heidelberg, 1999.","mla":"Deuflhard, Peter, et al. “Computation of Essential Molecular Dynamics by Subdivision Techniques.” Computational Molecular Dynamics: Challenges, Methods, Ideas, 1999, doi:10.1007/978-3-642-58360-5_5.","bibtex":"@inbook{Deuflhard_Dellnitz_Junge_Schütte_1999, place={Berlin, Heidelberg}, title={Computation of Essential Molecular Dynamics by Subdivision Techniques}, DOI={10.1007/978-3-642-58360-5_5}, booktitle={Computational Molecular Dynamics: Challenges, Methods, Ideas}, author={Deuflhard, Peter and Dellnitz, Michael and Junge, Oliver and Schütte, Christof}, year={1999} }","ama":"Deuflhard P, Dellnitz M, Junge O, Schütte C. Computation of Essential Molecular Dynamics by Subdivision Techniques. In: Computational Molecular Dynamics: Challenges, Methods, Ideas. Berlin, Heidelberg; 1999. doi:10.1007/978-3-642-58360-5_5","apa":"Deuflhard, P., Dellnitz, M., Junge, O., & Schütte, C. (1999). Computation of Essential Molecular Dynamics by Subdivision Techniques. In Computational Molecular Dynamics: Challenges, Methods, Ideas. Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58360-5_5","chicago":"Deuflhard, Peter, Michael Dellnitz, Oliver Junge, and Christof Schütte. “Computation of Essential Molecular Dynamics by Subdivision Techniques.” In Computational Molecular Dynamics: Challenges, Methods, Ideas. Berlin, Heidelberg, 1999. https://doi.org/10.1007/978-3-642-58360-5_5."},"type":"book_chapter"},{"language":[{"iso":"eng"}],"year":"2009","type":"journal_article","citation":{"bibtex":"@article{Dellnitz_Witting_2009, title={Computation of robust Pareto points}, DOI={10.1504/ijcsm.2009.027876}, number={243}, journal={International Journal of Computing Science and Mathematics}, author={Dellnitz, M. and Witting, K.}, year={2009} }","mla":"Dellnitz, M., and K. Witting. “Computation of Robust Pareto Points.” International Journal of Computing Science and Mathematics, 243, 2009, doi:10.1504/ijcsm.2009.027876.","ama":"Dellnitz M, Witting K. Computation of robust Pareto points. International Journal of Computing Science and Mathematics. 2009. doi:10.1504/ijcsm.2009.027876","apa":"Dellnitz, M., & Witting, K. (2009). Computation of robust Pareto points. International Journal of Computing Science and Mathematics. https://doi.org/10.1504/ijcsm.2009.027876","chicago":"Dellnitz, M., and K. Witting. “Computation of Robust Pareto Points.” International Journal of Computing Science and Mathematics, 2009. https://doi.org/10.1504/ijcsm.2009.027876.","ieee":"M. Dellnitz and K. Witting, “Computation of robust Pareto points,” International Journal of Computing Science and Mathematics, 2009.","short":"M. Dellnitz, K. Witting, International Journal of Computing Science and Mathematics (2009)."},"_id":"16545","date_updated":"2022-01-06T06:52:52Z","article_number":"243","doi":"10.1504/ijcsm.2009.027876","author":[{"first_name":"M.","full_name":"Dellnitz, M.","last_name":"Dellnitz"},{"last_name":"Witting","full_name":"Witting, K.","first_name":"K."}],"department":[{"_id":"101"}],"publication":"International Journal of Computing Science and Mathematics","status":"public","date_created":"2020-04-15T08:54:35Z","publication_identifier":{"issn":["1752-5055","1752-5063"]},"publication_status":"published","user_id":"15701","title":"Computation of robust Pareto points"},{"doi":"10.1098/rspa.2003.1143","_id":"16498","date_updated":"2022-01-06T06:52:51Z","type":"journal_article","citation":{"ieee":"P. J. Aston and M. Dellnitz, “Computation of the dominant Lyapunov exponent via spatial integration using matrix norms,” Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, pp. 2933–2955, 2003.","short":"P.J. Aston, M. Dellnitz, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences (2003) 2933–2955.","bibtex":"@article{Aston_Dellnitz_2003, title={Computation of the dominant Lyapunov exponent via spatial integration using matrix norms}, DOI={10.1098/rspa.2003.1143}, journal={Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences}, author={Aston, P. J. and Dellnitz, M.}, year={2003}, pages={2933–2955} }","mla":"Aston, P. J., and M. Dellnitz. “Computation of the Dominant Lyapunov Exponent via Spatial Integration Using Matrix Norms.” Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2003, pp. 2933–55, doi:10.1098/rspa.2003.1143.","chicago":"Aston, P. J., and M. Dellnitz. “Computation of the Dominant Lyapunov Exponent via Spatial Integration Using Matrix Norms.” Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2003, 2933–55. https://doi.org/10.1098/rspa.2003.1143.","ama":"Aston PJ, Dellnitz M. Computation of the dominant Lyapunov exponent via spatial integration using matrix norms. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences. 2003:2933-2955. doi:10.1098/rspa.2003.1143","apa":"Aston, P. J., & Dellnitz, M. (2003). Computation of the dominant Lyapunov exponent via spatial integration using matrix norms. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2933–2955. https://doi.org/10.1098/rspa.2003.1143"},"year":"2003","page":"2933-2955","language":[{"iso":"eng"}],"title":"Computation of the dominant Lyapunov exponent via spatial integration using matrix norms","user_id":"47427","publication_identifier":{"issn":["1364-5021","1471-2946"]},"publication_status":"published","status":"public","date_created":"2020-04-14T09:57:39Z","author":[{"last_name":"Aston","full_name":"Aston, P. J.","first_name":"P. J."},{"last_name":"Dellnitz","full_name":"Dellnitz, M.","first_name":"M."}],"department":[{"_id":"101"}],"publication":"Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences"},{"_id":"17012","date_updated":"2022-01-06T06:53:02Z","intvolume":" 12","doi":"10.1093/imanum/12.3.429","issue":"3","type":"journal_article","year":"1992","citation":{"bibtex":"@article{Dellnitz_1992, title={Computational bifurcation of periodic solutions in systems with symmetry}, volume={12}, DOI={10.1093/imanum/12.3.429}, number={3}, journal={IMA Journal of Numerical Analysis}, author={Dellnitz, Michael}, year={1992}, pages={429–455} }","mla":"Dellnitz, Michael. “Computational Bifurcation of Periodic Solutions in Systems with Symmetry.” IMA Journal of Numerical Analysis, vol. 12, no. 3, 1992, pp. 429–55, doi:10.1093/imanum/12.3.429.","chicago":"Dellnitz, Michael. “Computational Bifurcation of Periodic Solutions in Systems with Symmetry.” IMA Journal of Numerical Analysis 12, no. 3 (1992): 429–55. https://doi.org/10.1093/imanum/12.3.429.","ama":"Dellnitz M. Computational bifurcation of periodic solutions in systems with symmetry. IMA Journal of Numerical Analysis. 1992;12(3):429-455. doi:10.1093/imanum/12.3.429","apa":"Dellnitz, M. (1992). Computational bifurcation of periodic solutions in systems with symmetry. IMA Journal of Numerical Analysis, 12(3), 429–455. https://doi.org/10.1093/imanum/12.3.429","ieee":"M. Dellnitz, “Computational bifurcation of periodic solutions in systems with symmetry,” IMA Journal of Numerical Analysis, vol. 12, no. 3, pp. 429–455, 1992.","short":"M. Dellnitz, IMA Journal of Numerical Analysis 12 (1992) 429–455."},"page":"429-455","language":[{"iso":"eng"}],"title":"Computational bifurcation of periodic solutions in systems with symmetry","user_id":"32643","author":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"department":[{"_id":"101"}],"publication":"IMA Journal of Numerical Analysis","volume":12,"publication_status":"published","status":"public","date_created":"2020-05-19T08:53:14Z"},{"title":"Computational methods for bifurcation problems with symmetries—with special attention to steady state and Hopf bifurcation points","user_id":"15701","publication_identifier":{"issn":["0377-0427"]},"publication_status":"published","status":"public","date_created":"2020-04-16T10:28:09Z","author":[{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"last_name":"Werner","full_name":"Werner, Bodo","first_name":"Bodo"}],"department":[{"_id":"101"}],"publication":"Journal of Computational and Applied Mathematics","doi":"10.1016/0377-0427(89)90150-7","_id":"16682","date_updated":"2022-01-06T06:52:54Z","citation":{"bibtex":"@article{Dellnitz_Werner_1989, title={Computational methods for bifurcation problems with symmetries—with special attention to steady state and Hopf bifurcation points}, DOI={10.1016/0377-0427(89)90150-7}, journal={Journal of Computational and Applied Mathematics}, author={Dellnitz, Michael and Werner, Bodo}, year={1989}, pages={97–123} }","mla":"Dellnitz, Michael, and Bodo Werner. “Computational Methods for Bifurcation Problems with Symmetries—with Special Attention to Steady State and Hopf Bifurcation Points.” Journal of Computational and Applied Mathematics, 1989, pp. 97–123, doi:10.1016/0377-0427(89)90150-7.","ama":"Dellnitz M, Werner B. Computational methods for bifurcation problems with symmetries—with special attention to steady state and Hopf bifurcation points. Journal of Computational and Applied Mathematics. 1989:97-123. doi:10.1016/0377-0427(89)90150-7","apa":"Dellnitz, M., & Werner, B. (1989). Computational methods for bifurcation problems with symmetries—with special attention to steady state and Hopf bifurcation points. Journal of Computational and Applied Mathematics, 97–123. https://doi.org/10.1016/0377-0427(89)90150-7","chicago":"Dellnitz, Michael, and Bodo Werner. “Computational Methods for Bifurcation Problems with Symmetries—with Special Attention to Steady State and Hopf Bifurcation Points.” Journal of Computational and Applied Mathematics, 1989, 97–123. https://doi.org/10.1016/0377-0427(89)90150-7.","ieee":"M. Dellnitz and B. Werner, “Computational methods for bifurcation problems with symmetries—with special attention to steady state and Hopf bifurcation points,” Journal of Computational and Applied Mathematics, pp. 97–123, 1989.","short":"M. Dellnitz, B. Werner, Journal of Computational and Applied Mathematics (1989) 97–123."},"year":"1989","type":"journal_article","page":"97-123","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"page":"43-44","citation":{"short":"T. Gail, S. Leyendecker, S. Ober-Blöbaum, PAMM (2013) 43–44.","ieee":"T. Gail, S. Leyendecker, and S. Ober-Blöbaum, “Computing time investigations for variational multirate integration,” PAMM, pp. 43–44, 2013.","chicago":"Gail, Tobias, Sigrid Leyendecker, and Sina Ober-Blöbaum. “Computing Time Investigations for Variational Multirate Integration.” PAMM, 2013, 43–44. https://doi.org/10.1002/pamm.201310017.","ama":"Gail T, Leyendecker S, Ober-Blöbaum S. Computing time investigations for variational multirate integration. PAMM. 2013:43-44. doi:10.1002/pamm.201310017","apa":"Gail, T., Leyendecker, S., & Ober-Blöbaum, S. (2013). Computing time investigations for variational multirate integration. PAMM, 43–44. https://doi.org/10.1002/pamm.201310017","mla":"Gail, Tobias, et al. “Computing Time Investigations for Variational Multirate Integration.” PAMM, 2013, pp. 43–44, doi:10.1002/pamm.201310017.","bibtex":"@article{Gail_Leyendecker_Ober-Blöbaum_2013, title={Computing time investigations for variational multirate integration}, DOI={10.1002/pamm.201310017}, journal={PAMM}, author={Gail, Tobias and Leyendecker, Sigrid and Ober-Blöbaum, Sina}, year={2013}, pages={43–44} }"},"year":"2013","type":"journal_article","doi":"10.1002/pamm.201310017","date_updated":"2022-01-06T06:52:53Z","_id":"16608","date_created":"2020-04-16T07:58:09Z","status":"public","publication_status":"published","publication_identifier":{"issn":["1617-7061"]},"department":[{"_id":"101"}],"publication":"PAMM","author":[{"first_name":"Tobias","full_name":"Gail, Tobias","last_name":"Gail"},{"first_name":"Sigrid","full_name":"Leyendecker, Sigrid","last_name":"Leyendecker"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"}],"user_id":"15701","title":"Computing time investigations for variational multirate integration"},{"title":"Congestion and Almost Invariant Sets in Dynamical Systems","user_id":"15701","place":"Berlin, Heidelberg","publication_identifier":{"issn":["0302-9743"],"isbn":["9783540405542","9783540450849"]},"publication_status":"published","date_created":"2020-04-15T08:50:07Z","status":"public","publication":"Lecture Notes in Computer Science","department":[{"_id":"101"}],"author":[{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"},{"last_name":"Preis","first_name":"Robert","full_name":"Preis, Robert"}],"doi":"10.1007/3-540-45084-x_8","date_updated":"2022-01-06T06:52:52Z","_id":"16543","type":"book_chapter","year":"2003","citation":{"ieee":"M. Dellnitz and R. Preis, “Congestion and Almost Invariant Sets in Dynamical Systems,” in Lecture Notes in Computer Science, Berlin, Heidelberg, 2003.","short":"M. Dellnitz, R. Preis, in: Lecture Notes in Computer Science, Berlin, Heidelberg, 2003.","bibtex":"@inbook{Dellnitz_Preis_2003, place={Berlin, Heidelberg}, title={Congestion and Almost Invariant Sets in Dynamical Systems}, DOI={10.1007/3-540-45084-x_8}, booktitle={Lecture Notes in Computer Science}, author={Dellnitz, Michael and Preis, Robert}, year={2003} }","mla":"Dellnitz, Michael, and Robert Preis. “Congestion and Almost Invariant Sets in Dynamical Systems.” Lecture Notes in Computer Science, 2003, doi:10.1007/3-540-45084-x_8.","chicago":"Dellnitz, Michael, and Robert Preis. “Congestion and Almost Invariant Sets in Dynamical Systems.” In Lecture Notes in Computer Science. Berlin, Heidelberg, 2003. https://doi.org/10.1007/3-540-45084-x_8.","ama":"Dellnitz M, Preis R. Congestion and Almost Invariant Sets in Dynamical Systems. In: Lecture Notes in Computer Science. Berlin, Heidelberg; 2003. doi:10.1007/3-540-45084-x_8","apa":"Dellnitz, M., & Preis, R. (2003). Congestion and Almost Invariant Sets in Dynamical Systems. In Lecture Notes in Computer Science. Berlin, Heidelberg. https://doi.org/10.1007/3-540-45084-x_8"},"language":[{"iso":"eng"}]},{"doi":"10.1007/978-90-481-9884-9_12","_id":"16575","date_updated":"2022-01-06T06:52:52Z","year":"2010","type":"book_chapter","citation":{"ieee":"M. Dellnitz, K. Padberg, R. Preis, and B. Thiere, “Continuous and Discrete Concepts for Detecting Transport Barriers in the Planar Circular Restricted Three Body Problem,” in Nonlinear Science and Complexity, Dordrecht, 2010.","short":"M. Dellnitz, K. Padberg, R. Preis, B. Thiere, in: Nonlinear Science and Complexity, Dordrecht, 2010.","bibtex":"@inbook{Dellnitz_Padberg_Preis_Thiere_2010, place={Dordrecht}, title={Continuous and Discrete Concepts for Detecting Transport Barriers in the Planar Circular Restricted Three Body Problem}, DOI={10.1007/978-90-481-9884-9_12}, booktitle={Nonlinear Science and Complexity}, author={Dellnitz, Michael and Padberg, Kathrin and Preis, Robert and Thiere, Bianca}, year={2010} }","mla":"Dellnitz, Michael, et al. “Continuous and Discrete Concepts for Detecting Transport Barriers in the Planar Circular Restricted Three Body Problem.” Nonlinear Science and Complexity, 2010, doi:10.1007/978-90-481-9884-9_12.","ama":"Dellnitz M, Padberg K, Preis R, Thiere B. Continuous and Discrete Concepts for Detecting Transport Barriers in the Planar Circular Restricted Three Body Problem. In: Nonlinear Science and Complexity. Dordrecht; 2010. doi:10.1007/978-90-481-9884-9_12","apa":"Dellnitz, M., Padberg, K., Preis, R., & Thiere, B. (2010). Continuous and Discrete Concepts for Detecting Transport Barriers in the Planar Circular Restricted Three Body Problem. In Nonlinear Science and Complexity. Dordrecht. https://doi.org/10.1007/978-90-481-9884-9_12","chicago":"Dellnitz, Michael, Kathrin Padberg, Robert Preis, and Bianca Thiere. “Continuous and Discrete Concepts for Detecting Transport Barriers in the Planar Circular Restricted Three Body Problem.” In Nonlinear Science and Complexity. Dordrecht, 2010. https://doi.org/10.1007/978-90-481-9884-9_12."},"title":"Continuous and Discrete Concepts for Detecting Transport Barriers in the Planar Circular Restricted Three Body Problem","user_id":"15701","place":"Dordrecht","publication_identifier":{"isbn":["9789048198832","9789048198849"]},"publication_status":"published","status":"public","date_created":"2020-04-16T05:06:58Z","author":[{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"},{"last_name":"Padberg","first_name":"Kathrin","full_name":"Padberg, Kathrin"},{"first_name":"Robert","full_name":"Preis, Robert","last_name":"Preis"},{"last_name":"Thiere","first_name":"Bianca","full_name":"Thiere, Bianca"}],"publication":"Nonlinear Science and Complexity","department":[{"_id":"101"}]},{"publication_identifier":{"issn":["0924-090X","1573-269X"]},"publication_status":"published","status":"public","date_created":"2020-04-16T14:05:04Z","author":[{"first_name":"Tuhin","full_name":"Sahai, Tuhin","last_name":"Sahai"},{"first_name":"Adrian","full_name":"Ziessler, Adrian","last_name":"Ziessler"},{"first_name":"Stefan","full_name":"Klus, Stefan","last_name":"Klus"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"publication":"Nonlinear Dynamics","department":[{"_id":"101"}],"title":"Continuous relaxations for the traveling salesman problem","user_id":"47427","type":"journal_article","citation":{"ieee":"T. Sahai, A. Ziessler, S. Klus, and M. Dellnitz, “Continuous relaxations for the traveling salesman problem,” Nonlinear Dynamics, 2019.","short":"T. Sahai, A. Ziessler, S. Klus, M. Dellnitz, Nonlinear Dynamics (2019).","bibtex":"@article{Sahai_Ziessler_Klus_Dellnitz_2019, title={Continuous relaxations for the traveling salesman problem}, DOI={10.1007/s11071-019-05092-5}, journal={Nonlinear Dynamics}, author={Sahai, Tuhin and Ziessler, Adrian and Klus, Stefan and Dellnitz, Michael}, year={2019} }","mla":"Sahai, Tuhin, et al. “Continuous Relaxations for the Traveling Salesman Problem.” Nonlinear Dynamics, 2019, doi:10.1007/s11071-019-05092-5.","chicago":"Sahai, Tuhin, Adrian Ziessler, Stefan Klus, and Michael Dellnitz. “Continuous Relaxations for the Traveling Salesman Problem.” Nonlinear Dynamics, 2019. https://doi.org/10.1007/s11071-019-05092-5.","ama":"Sahai T, Ziessler A, Klus S, Dellnitz M. Continuous relaxations for the traveling salesman problem. Nonlinear Dynamics. 2019. doi:10.1007/s11071-019-05092-5","apa":"Sahai, T., Ziessler, A., Klus, S., & Dellnitz, M. (2019). Continuous relaxations for the traveling salesman problem. Nonlinear Dynamics. https://doi.org/10.1007/s11071-019-05092-5"},"year":"2019","language":[{"iso":"eng"}],"doi":"10.1007/s11071-019-05092-5","date_updated":"2022-01-06T06:52:55Z","_id":"16709"},{"language":[{"iso":"eng"}],"page":"1886-1905","type":"journal_article","citation":{"ieee":"K. Flaßkamp, J. Timmermann, S. Ober-Blöbaum, and A. Trächtler, “Control strategies on stable manifolds for energy-efficient swing-ups of double pendula,” International Journal of Control, pp. 1886–1905, 2014.","short":"K. Flaßkamp, J. Timmermann, S. Ober-Blöbaum, A. Trächtler, International Journal of Control (2014) 1886–1905.","mla":"Flaßkamp, Kathrin, et al. “Control Strategies on Stable Manifolds for Energy-Efficient Swing-Ups of Double Pendula.” International Journal of Control, 2014, pp. 1886–905, doi:10.1080/00207179.2014.893450.","bibtex":"@article{Flaßkamp_Timmermann_Ober-Blöbaum_Trächtler_2014, title={Control strategies on stable manifolds for energy-efficient swing-ups of double pendula}, DOI={10.1080/00207179.2014.893450}, journal={International Journal of Control}, author={Flaßkamp, Kathrin and Timmermann, Julia and Ober-Blöbaum, Sina and Trächtler, Ansgar}, year={2014}, pages={1886–1905} }","chicago":"Flaßkamp, Kathrin, Julia Timmermann, Sina Ober-Blöbaum, and Ansgar Trächtler. “Control Strategies on Stable Manifolds for Energy-Efficient Swing-Ups of Double Pendula.” International Journal of Control, 2014, 1886–1905. https://doi.org/10.1080/00207179.2014.893450.","ama":"Flaßkamp K, Timmermann J, Ober-Blöbaum S, Trächtler A. Control strategies on stable manifolds for energy-efficient swing-ups of double pendula. International Journal of Control. 2014:1886-1905. doi:10.1080/00207179.2014.893450","apa":"Flaßkamp, K., Timmermann, J., Ober-Blöbaum, S., & Trächtler, A. (2014). Control strategies on stable manifolds for energy-efficient swing-ups of double pendula. International Journal of Control, 1886–1905. https://doi.org/10.1080/00207179.2014.893450"},"year":"2014","doi":"10.1080/00207179.2014.893450","date_updated":"2022-01-06T06:52:52Z","_id":"16597","date_created":"2020-04-16T06:00:59Z","status":"public","publication_identifier":{"issn":["0020-7179","1366-5820"]},"publication_status":"published","department":[{"_id":"101"}],"publication":"International Journal of Control","author":[{"first_name":"Kathrin","full_name":"Flaßkamp, Kathrin","last_name":"Flaßkamp"},{"full_name":"Timmermann, Julia","first_name":"Julia","last_name":"Timmermann"},{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"},{"last_name":"Trächtler","full_name":"Trächtler, Ansgar","first_name":"Ansgar"}],"user_id":"15701","title":"Control strategies on stable manifolds for energy-efficient swing-ups of double pendula"},{"department":[{"_id":"101"}],"publication":"arXiv:1801.06419","author":[{"full_name":"Peitz, Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","first_name":"Sebastian","id":"47427","last_name":"Peitz"}],"date_created":"2020-03-13T12:43:14Z","status":"public","abstract":[{"text":"In a recent article, we presented a framework to control nonlinear partial\r\ndifferential equations (PDEs) by means of Koopman operator based reduced models\r\nand concepts from switched systems. The main idea was to transform a control\r\nsystem into a set of autonomous systems for which the optimal switching\r\nsequence has to be computed. These individual systems can be approximated very\r\nefficiently by reduced order models obtained from data, and one can guarantee\r\nequality of the full and the reduced objective function under certain\r\nassumptions. In this article, we extend these results to continuous control\r\ninputs using convex combinations of multiple Koopman operators corresponding to\r\nconstant controls, which results in a bilinear control system. Although\r\nequality of the objectives can be carried over when the PDE depends linearly on\r\nthe control, we show that this approach is also valid in other scenarios using\r\nseveral flow control examples of varying complexity.","lang":"eng"}],"title":"Controlling nonlinear PDEs using low-dimensional bilinear approximations obtained from data","user_id":"47427","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/1801.06419.pdf"}],"citation":{"ama":"Peitz S. Controlling nonlinear PDEs using low-dimensional bilinear approximations obtained from data. arXiv:180106419. 2018.","apa":"Peitz, S. (2018). Controlling nonlinear PDEs using low-dimensional bilinear approximations obtained from data. ArXiv:1801.06419.","chicago":"Peitz, Sebastian. “Controlling Nonlinear PDEs Using Low-Dimensional Bilinear Approximations Obtained from Data.” ArXiv:1801.06419, 2018.","mla":"Peitz, Sebastian. “Controlling Nonlinear PDEs Using Low-Dimensional Bilinear Approximations Obtained from Data.” ArXiv:1801.06419, 2018.","bibtex":"@article{Peitz_2018, title={Controlling nonlinear PDEs using low-dimensional bilinear approximations obtained from data}, journal={arXiv:1801.06419}, author={Peitz, Sebastian}, year={2018} }","short":"S. Peitz, ArXiv:1801.06419 (2018).","ieee":"S. Peitz, “Controlling nonlinear PDEs using low-dimensional bilinear approximations obtained from data,” arXiv:1801.06419. 2018."},"type":"preprint","year":"2018","language":[{"iso":"eng"}],"date_updated":"2022-01-06T06:52:48Z","_id":"16292","oa":"1"},{"date_updated":"2022-01-06T06:52:54Z","_id":"16668","doi":"10.1007/s10898-007-9265-7","language":[{"iso":"eng"}],"year":"2008","citation":{"ama":"Schütze O, Laumanns M, Coello Coello CA, Dellnitz M, Talbi E-G. Convergence of stochastic search algorithms to finite size pareto set approximations. Journal of Global Optimization. 2008:559-577. doi:10.1007/s10898-007-9265-7","apa":"Schütze, O., Laumanns, M., Coello Coello, C. A., Dellnitz, M., & Talbi, E.-G. (2008). Convergence of stochastic search algorithms to finite size pareto set approximations. Journal of Global Optimization, 559–577. https://doi.org/10.1007/s10898-007-9265-7","chicago":"Schütze, Oliver, Marco Laumanns, Carlos A. Coello Coello, Michael Dellnitz, and El-Ghazali Talbi. “Convergence of Stochastic Search Algorithms to Finite Size Pareto Set Approximations.” Journal of Global Optimization, 2008, 559–77. https://doi.org/10.1007/s10898-007-9265-7.","mla":"Schütze, Oliver, et al. “Convergence of Stochastic Search Algorithms to Finite Size Pareto Set Approximations.” Journal of Global Optimization, 2008, pp. 559–77, doi:10.1007/s10898-007-9265-7.","bibtex":"@article{Schütze_Laumanns_Coello Coello_Dellnitz_Talbi_2008, title={Convergence of stochastic search algorithms to finite size pareto set approximations}, DOI={10.1007/s10898-007-9265-7}, journal={Journal of Global Optimization}, author={Schütze, Oliver and Laumanns, Marco and Coello Coello, Carlos A. and Dellnitz, Michael and Talbi, El-Ghazali}, year={2008}, pages={559–577} }","short":"O. Schütze, M. Laumanns, C.A. Coello Coello, M. Dellnitz, E.-G. Talbi, Journal of Global Optimization (2008) 559–577.","ieee":"O. Schütze, M. Laumanns, C. A. Coello Coello, M. Dellnitz, and E.-G. Talbi, “Convergence of stochastic search algorithms to finite size pareto set approximations,” Journal of Global Optimization, pp. 559–577, 2008."},"type":"journal_article","page":"559-577","user_id":"15701","title":"Convergence of stochastic search algorithms to finite size pareto set approximations","author":[{"last_name":"Schütze","first_name":"Oliver","full_name":"Schütze, Oliver"},{"last_name":"Laumanns","full_name":"Laumanns, Marco","first_name":"Marco"},{"last_name":"Coello Coello","first_name":"Carlos A.","full_name":"Coello Coello, Carlos A."},{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"},{"last_name":"Talbi","full_name":"Talbi, El-Ghazali","first_name":"El-Ghazali"}],"department":[{"_id":"101"}],"publication":"Journal of Global Optimization","status":"public","date_created":"2020-04-16T10:02:17Z","publication_identifier":{"issn":["0925-5001","1573-2916"]},"publication_status":"published"},{"author":[{"last_name":"Schütze","full_name":"Schütze, Oliver","first_name":"Oliver"},{"last_name":"Mostaghim","first_name":"Sanaz","full_name":"Mostaghim, Sanaz"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"full_name":"Teich, Jürgen","first_name":"Jürgen","last_name":"Teich"}],"publication":"Lecture Notes in Computer Science","department":[{"_id":"101"}],"publication_status":"published","publication_identifier":{"issn":["0302-9743"],"isbn":["9783540018698","9783540369707"]},"status":"public","date_created":"2020-04-16T09:58:10Z","place":"Berlin, Heidelberg","title":"Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques","user_id":"15701","type":"book_chapter","citation":{"short":"O. Schütze, S. Mostaghim, M. Dellnitz, J. Teich, in: Lecture Notes in Computer Science, Berlin, Heidelberg, 2003.","ieee":"O. Schütze, S. Mostaghim, M. Dellnitz, and J. Teich, “Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques,” in Lecture Notes in Computer Science, Berlin, Heidelberg, 2003.","chicago":"Schütze, Oliver, Sanaz Mostaghim, Michael Dellnitz, and Jürgen Teich. “Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques.” In Lecture Notes in Computer Science. Berlin, Heidelberg, 2003. https://doi.org/10.1007/3-540-36970-8_9.","ama":"Schütze O, Mostaghim S, Dellnitz M, Teich J. Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques. In: Lecture Notes in Computer Science. Berlin, Heidelberg; 2003. doi:10.1007/3-540-36970-8_9","apa":"Schütze, O., Mostaghim, S., Dellnitz, M., & Teich, J. (2003). Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques. In Lecture Notes in Computer Science. Berlin, Heidelberg. https://doi.org/10.1007/3-540-36970-8_9","bibtex":"@inbook{Schütze_Mostaghim_Dellnitz_Teich_2003, place={Berlin, Heidelberg}, title={Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques}, DOI={10.1007/3-540-36970-8_9}, booktitle={Lecture Notes in Computer Science}, author={Schütze, Oliver and Mostaghim, Sanaz and Dellnitz, Michael and Teich, Jürgen}, year={2003} }","mla":"Schütze, Oliver, et al. “Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques.” Lecture Notes in Computer Science, 2003, doi:10.1007/3-540-36970-8_9."},"year":"2003","language":[{"iso":"eng"}],"date_updated":"2022-01-06T06:52:54Z","_id":"16665","doi":"10.1007/3-540-36970-8_9"},{"publication_identifier":{"issn":["0022-3239","1573-2878"]},"publication_status":"published","status":"public","date_created":"2020-04-16T10:31:32Z","author":[{"last_name":"Dellnitz","full_name":"Dellnitz, M.","first_name":"M."},{"last_name":"Sch�tze","first_name":"O.","full_name":"Sch�tze, O."},{"first_name":"T.","full_name":"Hestermeyer, T.","last_name":"Hestermeyer"}],"publication":"Journal of Optimization Theory and Applications","department":[{"_id":"101"}],"title":"Covering Pareto Sets by Multilevel Subdivision Techniques","user_id":"15701","year":"2005","citation":{"mla":"Dellnitz, M., et al. “Covering Pareto Sets by Multilevel Subdivision Techniques.” Journal of Optimization Theory and Applications, 2005, pp. 113–36, doi:10.1007/s10957-004-6468-7.","bibtex":"@article{Dellnitz_Sch�tze_Hestermeyer_2005, title={Covering Pareto Sets by Multilevel Subdivision Techniques}, DOI={10.1007/s10957-004-6468-7}, journal={Journal of Optimization Theory and Applications}, author={Dellnitz, M. and Sch�tze, O. and Hestermeyer, T.}, year={2005}, pages={113–136} }","apa":"Dellnitz, M., Sch�tze, O., & Hestermeyer, T. (2005). Covering Pareto Sets by Multilevel Subdivision Techniques. Journal of Optimization Theory and Applications, 113–136. https://doi.org/10.1007/s10957-004-6468-7","ama":"Dellnitz M, Sch�tze O, Hestermeyer T. Covering Pareto Sets by Multilevel Subdivision Techniques. Journal of Optimization Theory and Applications. 2005:113-136. doi:10.1007/s10957-004-6468-7","chicago":"Dellnitz, M., O. Sch�tze, and T. Hestermeyer. “Covering Pareto Sets by Multilevel Subdivision Techniques.” Journal of Optimization Theory and Applications, 2005, 113–36. https://doi.org/10.1007/s10957-004-6468-7.","ieee":"M. Dellnitz, O. Sch�tze, and T. Hestermeyer, “Covering Pareto Sets by Multilevel Subdivision Techniques,” Journal of Optimization Theory and Applications, pp. 113–136, 2005.","short":"M. Dellnitz, O. Sch�tze, T. Hestermeyer, Journal of Optimization Theory and Applications (2005) 113–136."},"type":"journal_article","page":"113-136","language":[{"iso":"eng"}],"doi":"10.1007/s10957-004-6468-7","_id":"16684","date_updated":"2022-01-06T06:52:54Z"},{"title":"Cycling Chaos","user_id":"15701","publication":"International Journal of Bifurcation and Chaos","department":[{"_id":"101"}],"author":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"last_name":"Field","full_name":"Field, Michael","first_name":"Michael"},{"last_name":"Golubitsky","first_name":"Martin","full_name":"Golubitsky, Martin"},{"first_name":"Jun","full_name":"Ma, Jun","last_name":"Ma"},{"first_name":"Andreas","full_name":"Hohmann, Andreas","last_name":"Hohmann"}],"publication_identifier":{"issn":["0218-1274","1793-6551"]},"publication_status":"published","date_created":"2020-04-15T09:04:16Z","status":"public","date_updated":"2022-01-06T06:52:52Z","_id":"16550","doi":"10.1142/s0218127495000909","page":"1243-1247","type":"journal_article","year":"1995","citation":{"ieee":"M. Dellnitz, M. Field, M. Golubitsky, J. Ma, and A. Hohmann, “Cycling Chaos,” International Journal of Bifurcation and Chaos, pp. 1243–1247, 1995.","short":"M. Dellnitz, M. Field, M. Golubitsky, J. Ma, A. Hohmann, International Journal of Bifurcation and Chaos (1995) 1243–1247.","mla":"Dellnitz, Michael, et al. “Cycling Chaos.” International Journal of Bifurcation and Chaos, 1995, pp. 1243–47, doi:10.1142/s0218127495000909.","bibtex":"@article{Dellnitz_Field_Golubitsky_Ma_Hohmann_1995, title={Cycling Chaos}, DOI={10.1142/s0218127495000909}, journal={International Journal of Bifurcation and Chaos}, author={Dellnitz, Michael and Field, Michael and Golubitsky, Martin and Ma, Jun and Hohmann, Andreas}, year={1995}, pages={1243–1247} }","chicago":"Dellnitz, Michael, Michael Field, Martin Golubitsky, Jun Ma, and Andreas Hohmann. “Cycling Chaos.” International Journal of Bifurcation and Chaos, 1995, 1243–47. https://doi.org/10.1142/s0218127495000909.","ama":"Dellnitz M, Field M, Golubitsky M, Ma J, Hohmann A. Cycling Chaos. International Journal of Bifurcation and Chaos. 1995:1243-1247. doi:10.1142/s0218127495000909","apa":"Dellnitz, M., Field, M., Golubitsky, M., Ma, J., & Hohmann, A. (1995). Cycling Chaos. International Journal of Bifurcation and Chaos, 1243–1247. https://doi.org/10.1142/s0218127495000909"},"language":[{"iso":"eng"}]},{"publication":"Physica D: Nonlinear Phenomena","department":[{"_id":"101"}],"author":[{"last_name":"Klus","full_name":"Klus, Stefan","first_name":"Stefan"},{"full_name":"Nüske, Feliks","orcid":"0000-0003-2444-7889","first_name":"Feliks","id":"81513","last_name":"Nüske"},{"orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian","id":"47427","last_name":"Peitz"},{"full_name":"Niemann, Jan-Hendrik","first_name":"Jan-Hendrik","last_name":"Niemann"},{"first_name":"Cecilia","full_name":"Clementi, Cecilia","last_name":"Clementi"},{"last_name":"Schütte","first_name":"Christof","full_name":"Schütte, Christof"}],"publication_status":"published","publication_identifier":{"issn":["0167-2789"]},"volume":406,"date_created":"2020-03-13T12:35:40Z","status":"public","abstract":[{"lang":"eng","text":"We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and stochastic dynamical systems. It can be used for computing eigenvalues, eigenfunctions, and modes of the generator and for system identification. In addition to learning the governing equations of deterministic systems, which then reduces to SINDy (sparse identification of nonlinear dynamics), it is possible to identify the drift and diffusion terms of stochastic differential equations from data. Moreover, we apply gEDMD to derive coarse-grained models of high-dimensional systems, and also to determine efficient model predictive control strategies. We highlight relationships with other methods and demonstrate the efficacy of the proposed methods using several guiding examples and prototypical molecular dynamics problems."}],"title":"Data-driven approximation of the Koopman generator: Model reduction, system identification, and control","user_id":"47427","year":"2020","citation":{"ieee":"S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, and C. Schütte, “Data-driven approximation of the Koopman generator: Model reduction, system identification, and control,” Physica D: Nonlinear Phenomena, vol. 406, 2020.","short":"S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, C. Schütte, Physica D: Nonlinear Phenomena 406 (2020).","bibtex":"@article{Klus_Nüske_Peitz_Niemann_Clementi_Schütte_2020, title={Data-driven approximation of the Koopman generator: Model reduction, system identification, and control}, volume={406}, DOI={10.1016/j.physd.2020.132416}, number={132416}, journal={Physica D: Nonlinear Phenomena}, author={Klus, Stefan and Nüske, Feliks and Peitz, Sebastian and Niemann, Jan-Hendrik and Clementi, Cecilia and Schütte, Christof}, year={2020} }","mla":"Klus, Stefan, et al. “Data-Driven Approximation of the Koopman Generator: Model Reduction, System Identification, and Control.” Physica D: Nonlinear Phenomena, vol. 406, 132416, 2020, doi:10.1016/j.physd.2020.132416.","ama":"Klus S, Nüske F, Peitz S, Niemann J-H, Clementi C, Schütte C. Data-driven approximation of the Koopman generator: Model reduction, system identification, and control. Physica D: Nonlinear Phenomena. 2020;406. doi:10.1016/j.physd.2020.132416","apa":"Klus, S., Nüske, F., Peitz, S., Niemann, J.-H., Clementi, C., & Schütte, C. (2020). Data-driven approximation of the Koopman generator: Model reduction, system identification, and control. Physica D: Nonlinear Phenomena, 406. https://doi.org/10.1016/j.physd.2020.132416","chicago":"Klus, Stefan, Feliks Nüske, Sebastian Peitz, Jan-Hendrik Niemann, Cecilia Clementi, and Christof Schütte. “Data-Driven Approximation of the Koopman Generator: Model Reduction, System Identification, and Control.” Physica D: Nonlinear Phenomena 406 (2020). https://doi.org/10.1016/j.physd.2020.132416."},"type":"journal_article","language":[{"iso":"eng"}],"date_updated":"2022-01-06T06:52:48Z","_id":"16288","intvolume":" 406","doi":"10.1016/j.physd.2020.132416","article_number":"132416"},{"doi":"10.1137/20M1325678","issue":"3","_id":"16309","date_updated":"2022-01-06T06:52:48Z","intvolume":" 19","year":"2020","type":"journal_article","citation":{"bibtex":"@article{Peitz_Otto_Rowley_2020, title={Data-Driven Model Predictive Control using Interpolated Koopman Generators}, volume={19}, DOI={10.1137/20M1325678}, number={3}, journal={SIAM Journal on Applied Dynamical Systems}, author={Peitz, Sebastian and Otto, Samuel E. and Rowley, Clarence W.}, year={2020}, pages={2162–2193} }","mla":"Peitz, Sebastian, et al. “Data-Driven Model Predictive Control Using Interpolated Koopman Generators.” SIAM Journal on Applied Dynamical Systems, vol. 19, no. 3, 2020, pp. 2162–93, doi:10.1137/20M1325678.","apa":"Peitz, S., Otto, S. E., & Rowley, C. W. (2020). Data-Driven Model Predictive Control using Interpolated Koopman Generators. SIAM Journal on Applied Dynamical Systems, 19(3), 2162–2193. https://doi.org/10.1137/20M1325678","ama":"Peitz S, Otto SE, Rowley CW. Data-Driven Model Predictive Control using Interpolated Koopman Generators. SIAM Journal on Applied Dynamical Systems. 2020;19(3):2162-2193. doi:10.1137/20M1325678","chicago":"Peitz, Sebastian, Samuel E. Otto, and Clarence W. Rowley. “Data-Driven Model Predictive Control Using Interpolated Koopman Generators.” SIAM Journal on Applied Dynamical Systems 19, no. 3 (2020): 2162–93. https://doi.org/10.1137/20M1325678.","ieee":"S. Peitz, S. E. Otto, and C. W. Rowley, “Data-Driven Model Predictive Control using Interpolated Koopman Generators,” SIAM Journal on Applied Dynamical Systems, vol. 19, no. 3, pp. 2162–2193, 2020.","short":"S. Peitz, S.E. Otto, C.W. Rowley, SIAM Journal on Applied Dynamical Systems 19 (2020) 2162–2193."},"page":"2162-2193","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://epubs.siam.org/doi/pdf/10.1137/20M1325678"}],"title":"Data-Driven Model Predictive Control using Interpolated Koopman Generators","user_id":"47427","abstract":[{"lang":"eng","text":"In recent years, the success of the Koopman operator in dynamical systems\r\nanalysis has also fueled the development of Koopman operator-based control\r\nframeworks. In order to preserve the relatively low data requirements for an\r\napproximation via Dynamic Mode Decomposition, a quantization approach was\r\nrecently proposed in [Peitz & Klus, Automatica 106, 2019]. This way, control\r\nof nonlinear dynamical systems can be realized by means of switched systems\r\ntechniques, using only a finite set of autonomous Koopman operator-based\r\nreduced models. These individual systems can be approximated very efficiently\r\nfrom data. The main idea is to transform a control system into a set of\r\nautonomous systems for which the optimal switching sequence has to be computed.\r\nIn this article, we extend these results to continuous control inputs using\r\nrelaxation. This way, we combine the advantages of the data efficiency of\r\napproximating a finite set of autonomous systems with continuous controls. We\r\nshow that when using the Koopman generator, this relaxation --- realized by\r\nlinear interpolation between two operators --- does not introduce any error for\r\ncontrol affine systems. This allows us to control high-dimensional nonlinear\r\nsystems using bilinear, low-dimensional surrogate models. The efficiency of the\r\nproposed approach is demonstrated using several examples with increasing\r\ncomplexity, from the Duffing oscillator to the chaotic fluidic pinball."}],"volume":19,"status":"public","date_created":"2020-03-17T09:53:01Z","author":[{"first_name":"Sebastian","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","last_name":"Peitz","id":"47427"},{"last_name":"Otto","first_name":"Samuel E.","full_name":"Otto, Samuel E."},{"first_name":"Clarence W.","full_name":"Rowley, Clarence W.","last_name":"Rowley"}],"department":[{"_id":"101"}],"publication":"SIAM Journal on Applied Dynamical Systems"},{"language":[{"iso":"eng"}],"page":"985-1010","year":"2018","citation":{"bibtex":"@article{Klus_Nüske_Koltai_Wu_Kevrekidis_Schütte_Noé_2018, title={Data-Driven Model Reduction and Transfer Operator Approximation}, DOI={10.1007/s00332-017-9437-7}, journal={Journal of Nonlinear Science}, author={Klus, Stefan and Nüske, Feliks and Koltai, Péter and Wu, Hao and Kevrekidis, Ioannis and Schütte, Christof and Noé, Frank}, year={2018}, pages={985–1010} }","mla":"Klus, Stefan, et al. “Data-Driven Model Reduction and Transfer Operator Approximation.” Journal of Nonlinear Science, 2018, pp. 985–1010, doi:10.1007/s00332-017-9437-7.","ama":"Klus S, Nüske F, Koltai P, et al. Data-Driven Model Reduction and Transfer Operator Approximation. Journal of Nonlinear Science. 2018:985-1010. doi:10.1007/s00332-017-9437-7","apa":"Klus, S., Nüske, F., Koltai, P., Wu, H., Kevrekidis, I., Schütte, C., & Noé, F. (2018). Data-Driven Model Reduction and Transfer Operator Approximation. Journal of Nonlinear Science, 985–1010. https://doi.org/10.1007/s00332-017-9437-7","chicago":"Klus, Stefan, Feliks Nüske, Péter Koltai, Hao Wu, Ioannis Kevrekidis, Christof Schütte, and Frank Noé. “Data-Driven Model Reduction and Transfer Operator Approximation.” Journal of Nonlinear Science, 2018, 985–1010. https://doi.org/10.1007/s00332-017-9437-7.","ieee":"S. Klus et al., “Data-Driven Model Reduction and Transfer Operator Approximation,” Journal of Nonlinear Science, pp. 985–1010, 2018.","short":"S. Klus, F. Nüske, P. Koltai, H. Wu, I. Kevrekidis, C. Schütte, F. Noé, Journal of Nonlinear Science (2018) 985–1010."},"type":"journal_article","doi":"10.1007/s00332-017-9437-7","_id":"21941","date_updated":"2022-01-06T06:55:20Z","date_created":"2021-04-30T16:59:03Z","status":"public","publication_identifier":{"issn":["0938-8974","1432-1467"]},"publication_status":"published","publication":"Journal of Nonlinear Science","department":[{"_id":"101"}],"author":[{"last_name":"Klus","first_name":"Stefan","full_name":"Klus, Stefan"},{"id":"81513","last_name":"Nüske","orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks","first_name":"Feliks"},{"last_name":"Koltai","first_name":"Péter","full_name":"Koltai, Péter"},{"full_name":"Wu, Hao","first_name":"Hao","last_name":"Wu"},{"last_name":"Kevrekidis","full_name":"Kevrekidis, Ioannis","first_name":"Ioannis"},{"last_name":"Schütte","full_name":"Schütte, Christof","first_name":"Christof"},{"first_name":"Frank","full_name":"Noé, Frank","last_name":"Noé"}],"user_id":"81513","title":"Data-Driven Model Reduction and Transfer Operator Approximation","extern":"1"},{"intvolume":" 34","_id":"16290","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s00162-020-00520-4.pdf"}],"page":"577–591","type":"journal_article","year":"2020","citation":{"ieee":"K. Bieker, S. Peitz, S. L. Brunton, J. N. Kutz, and M. Dellnitz, “Deep model predictive flow control with limited sensor data and online learning,” Theoretical and Computational Fluid Dynamics, vol. 34, pp. 577–591, 2020.","short":"K. Bieker, S. Peitz, S.L. Brunton, J.N. Kutz, M. Dellnitz, Theoretical and Computational Fluid Dynamics 34 (2020) 577–591.","mla":"Bieker, Katharina, et al. “Deep Model Predictive Flow Control with Limited Sensor Data and Online Learning.” Theoretical and Computational Fluid Dynamics, vol. 34, 2020, pp. 577–591, doi:10.1007/s00162-020-00520-4.","bibtex":"@article{Bieker_Peitz_Brunton_Kutz_Dellnitz_2020, title={Deep model predictive flow control with limited sensor data and online learning}, volume={34}, DOI={10.1007/s00162-020-00520-4}, journal={Theoretical and Computational Fluid Dynamics}, author={Bieker, Katharina and Peitz, Sebastian and Brunton, Steven L. and Kutz, J. Nathan and Dellnitz, Michael}, year={2020}, pages={577–591} }","chicago":"Bieker, Katharina, Sebastian Peitz, Steven L. Brunton, J. Nathan Kutz, and Michael Dellnitz. “Deep Model Predictive Flow Control with Limited Sensor Data and Online Learning.” Theoretical and Computational Fluid Dynamics 34 (2020): 577–591. https://doi.org/10.1007/s00162-020-00520-4.","ama":"Bieker K, Peitz S, Brunton SL, Kutz JN, Dellnitz M. Deep model predictive flow control with limited sensor data and online learning. Theoretical and Computational Fluid Dynamics. 2020;34:577–591. doi:10.1007/s00162-020-00520-4","apa":"Bieker, K., Peitz, S., Brunton, S. L., Kutz, J. N., & Dellnitz, M. (2020). Deep model predictive flow control with limited sensor data and online learning. Theoretical and Computational Fluid Dynamics, 34, 577–591. https://doi.org/10.1007/s00162-020-00520-4"},"abstract":[{"text":"The control of complex systems is of critical importance in many branches of science, engineering, and industry, many of which are governed by nonlinear partial differential equations. Controlling an unsteady fluid flow is particularly important, as flow control is a key enabler for technologies in energy (e.g., wind, tidal, and combustion), transportation (e.g., planes, trains, and automobiles), security (e.g., tracking airborne contamination), and health (e.g., artificial hearts and artificial respiration). However, the high-dimensional, nonlinear, and multi-scale dynamics make real-time feedback control infeasible. Fortunately, these high- dimensional systems exhibit dominant, low-dimensional patterns of activity that can be exploited for effective control in the sense that knowledge of the entire state of a system is not required. Advances in machine learning have the potential to revolutionize flow control given its ability to extract principled, low-rank feature spaces characterizing such complex systems.We present a novel deep learning modelpredictive control framework that exploits low-rank features of the flow in order to achieve considerable improvements to control performance. Instead of predicting the entire fluid state, we use a recurrent neural network (RNN) to accurately predict the control relevant quantities of the system, which are then embedded into an MPC framework to construct a feedback loop. In order to lower the data requirements and to improve the prediction accuracy and thus the control performance, incoming sensor data are used to update the RNN online. The results are validated using varying fluid flow examples of increasing complexity.","lang":"eng"}],"article_type":"original","user_id":"47427","publication":"Theoretical and Computational Fluid Dynamics","author":[{"first_name":"Katharina","full_name":"Bieker, Katharina","last_name":"Bieker","id":"32829"},{"id":"47427","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian"},{"last_name":"Brunton","full_name":"Brunton, Steven L.","first_name":"Steven L."},{"last_name":"Kutz","full_name":"Kutz, J. Nathan","first_name":"J. Nathan"},{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"}],"date_created":"2020-03-13T12:40:09Z","status":"public","volume":34,"date_updated":"2022-01-06T06:52:48Z","oa":"1","doi":"10.1007/s00162-020-00520-4","language":[{"iso":"eng"}],"title":"Deep model predictive flow control with limited sensor data and online learning","department":[{"_id":"101"}],"project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"publication_status":"published","publication_identifier":{"issn":["0935-4964","1432-2250"]}},{"volume":26,"date_created":"2021-03-01T10:46:48Z","status":"public","publication":"Mathematical and Computational Applications","author":[{"id":"51701","last_name":"Berkemeier","full_name":"Berkemeier, Manuel Bastian","first_name":"Manuel Bastian"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427"}],"user_id":"47427","abstract":[{"text":"We present a flexible trust region descend algorithm for unconstrained and\r\nconvexly constrained multiobjective optimization problems. It is targeted at\r\nheterogeneous and expensive problems, i.e., problems that have at least one\r\nobjective function that is computationally expensive. The method is\r\nderivative-free in the sense that neither need derivative information be\r\navailable for the expensive objectives nor are gradients approximated using\r\nrepeated function evaluations as is the case in finite-difference methods.\r\nInstead, a multiobjective trust region approach is used that works similarly to\r\nits well-known scalar pendants. Local surrogate models constructed from\r\nevaluation data of the true objective functions are employed to compute\r\npossible descent directions. In contrast to existing multiobjective trust\r\nregion algorithms, these surrogates are not polynomial but carefully\r\nconstructed radial basis function networks. This has the important advantage\r\nthat the number of data points scales linearly with the parameter space\r\ndimension. The local models qualify as fully linear and the corresponding\r\ngeneral scalar framework is adapted for problems with multiple objectives.\r\nConvergence to Pareto critical points is proven and numerical examples\r\nillustrate our findings.","lang":"eng"}],"year":"2021","type":"journal_article","citation":{"ieee":"M. B. Berkemeier and S. Peitz, “Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models,” Mathematical and Computational Applications, vol. 26, no. 2, 2021.","short":"M.B. Berkemeier, S. Peitz, Mathematical and Computational Applications 26 (2021).","mla":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models.” Mathematical and Computational Applications, vol. 26, no. 2, 31, 2021, doi:10.3390/mca26020031.","bibtex":"@article{Berkemeier_Peitz_2021, title={Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models}, volume={26}, DOI={10.3390/mca26020031}, number={231}, journal={Mathematical and Computational Applications}, author={Berkemeier, Manuel Bastian and Peitz, Sebastian}, year={2021} }","apa":"Berkemeier, M. B., & Peitz, S. (2021). Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models. Mathematical and Computational Applications, 26(2). https://doi.org/10.3390/mca26020031","ama":"Berkemeier MB, Peitz S. Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models. Mathematical and Computational Applications. 2021;26(2). doi:10.3390/mca26020031","chicago":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models.” Mathematical and Computational Applications 26, no. 2 (2021). https://doi.org/10.3390/mca26020031."},"main_file_link":[{"url":"https://www.mdpi.com/2297-8747/26/2/31/pdf","open_access":"1"}],"article_number":"31","issue":"2","_id":"21337","intvolume":" 26","publication_identifier":{"eissn":["2297-8747"]},"publication_status":"published","department":[{"_id":"101"},{"_id":"655"}],"title":"Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models","language":[{"iso":"eng"}],"doi":"10.3390/mca26020031","oa":"1","date_updated":"2022-01-06T06:54:55Z"},{"year":"2005","citation":{"chicago":"Li, R., A. Pottharst, N. Frohieke, J. Becker, K. Witting, M. Dellnitz, O. Znamenshchykov, and R. Feldmann. “Design and Implementation of a Hybrid Energy Supply System for Railway Vehicles.” In Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005., 2005. https://doi.org/10.1109/apec.2005.1452979.","ama":"Li R, Pottharst A, Frohieke N, et al. Design and implementation of a hybrid energy supply system for railway vehicles. In: Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005. ; 2005. doi:10.1109/apec.2005.1452979","apa":"Li, R., Pottharst, A., Frohieke, N., Becker, J., Witting, K., Dellnitz, M., … Feldmann, R. (2005). Design and implementation of a hybrid energy supply system for railway vehicles. In Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005. https://doi.org/10.1109/apec.2005.1452979","bibtex":"@inproceedings{Li_Pottharst_Frohieke_Becker_Witting_Dellnitz_Znamenshchykov_Feldmann_2005, title={Design and implementation of a hybrid energy supply system for railway vehicles}, DOI={10.1109/apec.2005.1452979}, booktitle={Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005.}, author={Li, R. and Pottharst, A. and Frohieke, N. and Becker, J. and Witting, K. and Dellnitz, M. and Znamenshchykov, O. and Feldmann, R.}, year={2005} }","mla":"Li, R., et al. “Design and Implementation of a Hybrid Energy Supply System for Railway Vehicles.” Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005., 2005, doi:10.1109/apec.2005.1452979.","short":"R. Li, A. Pottharst, N. Frohieke, J. Becker, K. Witting, M. Dellnitz, O. Znamenshchykov, R. Feldmann, in: Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005., 2005.","ieee":"R. Li et al., “Design and implementation of a hybrid energy supply system for railway vehicles,” in Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005., 2005."},"type":"conference","doi":"10.1109/apec.2005.1452979","_id":"16631","date_updated":"2022-01-06T06:52:53Z","date_created":"2020-04-16T08:29:47Z","status":"public","publication_identifier":{"isbn":["0780389751"]},"publication_status":"published","publication":"Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005.","department":[{"_id":"101"}],"author":[{"full_name":"Li, R.","first_name":"R.","last_name":"Li"},{"last_name":"Pottharst","first_name":"A.","full_name":"Pottharst, A."},{"last_name":"Frohieke","first_name":"N.","full_name":"Frohieke, N."},{"full_name":"Becker, J.","first_name":"J.","last_name":"Becker"},{"last_name":"Witting","first_name":"K.","full_name":"Witting, K."},{"first_name":"M.","full_name":"Dellnitz, M.","last_name":"Dellnitz"},{"full_name":"Znamenshchykov, O.","first_name":"O.","last_name":"Znamenshchykov"},{"full_name":"Feldmann, R.","first_name":"R.","last_name":"Feldmann"}],"user_id":"15701","title":"Design and implementation of a hybrid energy supply system for railway vehicles"},{"department":[{"_id":"101"}],"publication":"Engineering Optimization","author":[{"last_name":"Schütze","full_name":"Schütze, Oliver","first_name":"Oliver"},{"last_name":"Vasile","full_name":"Vasile, Massimiliano","first_name":"Massimiliano"},{"last_name":"Junge","full_name":"Junge, Oliver","first_name":"Oliver"},{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"},{"last_name":"Izzo","full_name":"Izzo, Dario","first_name":"Dario"}],"date_created":"2020-04-16T10:04:50Z","status":"public","publication_identifier":{"issn":["0305-215X","1029-0273"]},"publication_status":"published","user_id":"15701","title":"Designing optimal low-thrust gravity-assist trajectories using space pruning and a multi-objective approach","language":[{"iso":"eng"}],"page":"155-181","type":"journal_article","citation":{"short":"O. Schütze, M. Vasile, O. Junge, M. Dellnitz, D. Izzo, Engineering Optimization (2009) 155–181.","ieee":"O. Schütze, M. Vasile, O. Junge, M. Dellnitz, and D. Izzo, “Designing optimal low-thrust gravity-assist trajectories using space pruning and a multi-objective approach,” Engineering Optimization, pp. 155–181, 2009.","chicago":"Schütze, Oliver, Massimiliano Vasile, Oliver Junge, Michael Dellnitz, and Dario Izzo. “Designing Optimal Low-Thrust Gravity-Assist Trajectories Using Space Pruning and a Multi-Objective Approach.” Engineering Optimization, 2009, 155–81. https://doi.org/10.1080/03052150802391734.","ama":"Schütze O, Vasile M, Junge O, Dellnitz M, Izzo D. Designing optimal low-thrust gravity-assist trajectories using space pruning and a multi-objective approach. Engineering Optimization. 2009:155-181. doi:10.1080/03052150802391734","apa":"Schütze, O., Vasile, M., Junge, O., Dellnitz, M., & Izzo, D. (2009). Designing optimal low-thrust gravity-assist trajectories using space pruning and a multi-objective approach. Engineering Optimization, 155–181. https://doi.org/10.1080/03052150802391734","bibtex":"@article{Schütze_Vasile_Junge_Dellnitz_Izzo_2009, title={Designing optimal low-thrust gravity-assist trajectories using space pruning and a multi-objective approach}, DOI={10.1080/03052150802391734}, journal={Engineering Optimization}, author={Schütze, Oliver and Vasile, Massimiliano and Junge, Oliver and Dellnitz, Michael and Izzo, Dario}, year={2009}, pages={155–181} }","mla":"Schütze, Oliver, et al. “Designing Optimal Low-Thrust Gravity-Assist Trajectories Using Space Pruning and a Multi-Objective Approach.” Engineering Optimization, 2009, pp. 155–81, doi:10.1080/03052150802391734."},"year":"2009","_id":"16669","date_updated":"2022-01-06T06:52:54Z","doi":"10.1080/03052150802391734"},{"page":"1839-1863","year":"2003","citation":{"ieee":"G. Froyland and M. Dellnitz, “Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles,” SIAM Journal on Scientific Computing, pp. 1839–1863, 2003.","short":"G. Froyland, M. Dellnitz, SIAM Journal on Scientific Computing (2003) 1839–1863.","mla":"Froyland, Gary, and Michael Dellnitz. “Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles.” SIAM Journal on Scientific Computing, 2003, pp. 1839–63, doi:10.1137/s106482750238911x.","bibtex":"@article{Froyland_Dellnitz_2003, title={Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles}, DOI={10.1137/s106482750238911x}, journal={SIAM Journal on Scientific Computing}, author={Froyland, Gary and Dellnitz, Michael}, year={2003}, pages={1839–1863} }","chicago":"Froyland, Gary, and Michael Dellnitz. “Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles.” SIAM Journal on Scientific Computing, 2003, 1839–63. https://doi.org/10.1137/s106482750238911x.","apa":"Froyland, G., & Dellnitz, M. (2003). Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles. SIAM Journal on Scientific Computing, 1839–1863. https://doi.org/10.1137/s106482750238911x","ama":"Froyland G, Dellnitz M. Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles. 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(2010). Detecting Initial Guesses for Trajectories in the (P)CRTBP. In AIAA/AAS Astrodynamics Specialist Conference. https://doi.org/10.2514/6.2010-7962","ama":"Thiere B, Ober-Blöbaum S, Pergola P. Detecting Initial Guesses for Trajectories in the (P)CRTBP. In: AIAA/AAS Astrodynamics Specialist Conference. ; 2010. doi:10.2514/6.2010-7962","chicago":"Thiere, Bianca, Sina Ober-Blöbaum, and Pierpaolo Pergola. “Detecting Initial Guesses for Trajectories in the (P)CRTBP.” In AIAA/AAS Astrodynamics Specialist Conference, 2010. https://doi.org/10.2514/6.2010-7962.","ieee":"B. Thiere, S. Ober-Blöbaum, and P. Pergola, “Detecting Initial Guesses for Trajectories in the (P)CRTBP,” in AIAA/AAS Astrodynamics Specialist Conference, 2010.","short":"B. Thiere, S. Ober-Blöbaum, P. 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It is shown that this respect for the mechanical structure (such as a reliable computation of the energy and momentum budget, without numerical dissipation) is retained when the system is reduced to its minimal dimension by the discrete null space method. Together with initial and final conditions on the configuration and conjugate momentum, the reduced time-stepping equations serve as nonlinear equality constraints for the minimisation of a given cost functional. The algorithm yields a sequence of discrete configurations together with a sequence of actuating forces, optimally guiding the system from the initial to the desired final state. 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Witting, in: 2008 19th International Conference on Database and Expert Systems Applications, 2008.","bibtex":"@inproceedings{Klöpper_Podlogar_Gausemeier_Witting_2008, title={Domain Spanning Search for the Identification of Solution Patterns for the Conceptual Design of Self-Optimizing Systems}, DOI={10.1109/dexa.2008.111}, booktitle={2008 19th International Conference on Database and Expert Systems Applications}, author={Klöpper, Benjamin and Podlogar, Herbert and Gausemeier, Jürgen and Witting, Katrin}, year={2008} }","mla":"Klöpper, Benjamin, et al. “Domain Spanning Search for the Identification of Solution Patterns for the Conceptual Design of Self-Optimizing Systems.” 2008 19th International Conference on Database and Expert Systems Applications, 2008, doi:10.1109/dexa.2008.111.","chicago":"Klöpper, Benjamin, Herbert Podlogar, Jürgen Gausemeier, and Katrin Witting. “Domain Spanning Search for the Identification of Solution Patterns for the Conceptual Design of Self-Optimizing Systems.” In 2008 19th International Conference on Database and Expert Systems Applications, 2008. https://doi.org/10.1109/dexa.2008.111.","ama":"Klöpper B, Podlogar H, Gausemeier J, Witting K. 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In 2008 19th International Conference on Database and Expert Systems Applications. https://doi.org/10.1109/dexa.2008.111"},"year":"2008"},{"date_created":"2021-04-09T07:59:19Z","has_accepted_license":"1","status":"public","volume":45,"publication":"SIAM Journal on Scientific Computing","author":[{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"last_name":"Hüllermeier","id":"48129","first_name":"Eyke","full_name":"Hüllermeier, Eyke"},{"last_name":"Lücke","first_name":"Marvin","full_name":"Lücke, Marvin"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","id":"16494","last_name":"Ober-Blöbaum"},{"id":"85279","last_name":"Offen","full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","first_name":"Christian"},{"id":"47427","last_name":"Peitz","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian"},{"last_name":"Pfannschmidt","id":"13472","first_name":"Karlson","full_name":"Pfannschmidt, Karlson","orcid":"0000-0001-9407-7903"}],"user_id":"47427","ddc":["510"],"abstract":[{"lang":"eng","text":"Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it results in prohibitively large errors or computational effort. To this end, adaptive schemes, such as solvers based on Runge–Kutta pairs, have been developed which adapt the step size based on local error estimations at each step. While the classical schemes apply very generally and are highly efficient on regular systems, they can behave suboptimally when an inefficient step rejection mechanism is triggered by structurally complex systems such as chaotic systems. To overcome these issues, we propose a method to tailor numerical schemes to the problem class at hand. This is achieved by combining simple, classical quadrature rules or ODE solvers with data-driven time-stepping controllers. Compared with learning solution operators to ODEs directly, it generalizes better to unseen initial data as our approach employs classical numerical schemes as base methods. At the same time it can make use of identified structures of a problem class and, therefore, outperforms state-of-the-art adaptive schemes. Several examples demonstrate superior efficiency. Source code is available at https://github.com/lueckem/quadrature-ML."}],"page":"A579-A595","type":"journal_article","year":"2023","citation":{"mla":"Dellnitz, Michael, et al. “Efficient Time Stepping for Numerical Integration Using Reinforcement Learning.” SIAM Journal on Scientific Computing, vol. 45, no. 2, 2023, pp. A579–95, doi:10.1137/21M1412682.","bibtex":"@article{Dellnitz_Hüllermeier_Lücke_Ober-Blöbaum_Offen_Peitz_Pfannschmidt_2023, title={Efficient time stepping for numerical integration using reinforcement learning}, volume={45}, DOI={10.1137/21M1412682}, number={2}, journal={SIAM Journal on Scientific Computing}, author={Dellnitz, Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen, Christian and Peitz, Sebastian and Pfannschmidt, Karlson}, year={2023}, pages={A579–A595} }","ama":"Dellnitz M, Hüllermeier E, Lücke M, et al. Efficient time stepping for numerical integration using reinforcement learning. SIAM Journal on Scientific Computing. 2023;45(2):A579-A595. doi:10.1137/21M1412682","apa":"Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz, S., & Pfannschmidt, K. (2023). Efficient time stepping for numerical integration using reinforcement learning. SIAM Journal on Scientific Computing, 45(2), A579–A595. https://doi.org/10.1137/21M1412682","chicago":"Dellnitz, Michael, Eyke Hüllermeier, Marvin Lücke, Sina Ober-Blöbaum, Christian Offen, Sebastian Peitz, and Karlson Pfannschmidt. “Efficient Time Stepping for Numerical Integration Using Reinforcement Learning.” SIAM Journal on Scientific Computing 45, no. 2 (2023): A579–95. https://doi.org/10.1137/21M1412682.","ieee":"M. Dellnitz et al., “Efficient time stepping for numerical integration using reinforcement learning,” SIAM Journal on Scientific Computing, vol. 45, no. 2, pp. A579–A595, 2023, doi: 10.1137/21M1412682.","short":"M. Dellnitz, E. Hüllermeier, M. Lücke, S. Ober-Blöbaum, C. Offen, S. Peitz, K. Pfannschmidt, SIAM Journal on Scientific Computing 45 (2023) A579–A595."},"main_file_link":[{"url":"https://epubs.siam.org/doi/reader/10.1137/21M1412682"}],"issue":"2","_id":"21600","intvolume":" 45","publication_status":"published","department":[{"_id":"101"},{"_id":"636"},{"_id":"355"},{"_id":"655"}],"related_material":{"link":[{"relation":"software","description":"GitHub","url":"https://github.com/lueckem/quadrature-ML"}]},"title":"Efficient time stepping for numerical integration using reinforcement learning","external_id":{"arxiv":["arXiv:2104.03562"]},"language":[{"iso":"eng"}],"doi":"10.1137/21M1412682","date_updated":"2023-08-25T09:24:50Z"},{"_id":"30294","intvolume":" 35","year":"2022","type":"book_chapter","citation":{"chicago":"Peitz, Sebastian, Michael Dellnitz, and Sebastian Bannenberg. “Efficient Virtual Design and Testing of Autonomous Vehicles.” In German Success Stories in Industrial Mathematics, edited by H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, and V. Schulz, Vol. 35. Mathematics in Industry. Cham: Springer International Publishing, 2022. https://doi.org/10.1007/978-3-030-81455-7_23.","apa":"Peitz, S., Dellnitz, M., & Bannenberg, S. (2022). Efficient Virtual Design and Testing of Autonomous Vehicles. In H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, & V. Schulz (Eds.), German Success Stories in Industrial Mathematics (Vol. 35). Springer International Publishing. https://doi.org/10.1007/978-3-030-81455-7_23","ama":"Peitz S, Dellnitz M, Bannenberg S. Efficient Virtual Design and Testing of Autonomous Vehicles. In: Bock HG, Küfer K-H, Maas P, Milde A, Schulz V, eds. German Success Stories in Industrial Mathematics. Vol 35. Mathematics in Industry. Springer International Publishing; 2022. doi:10.1007/978-3-030-81455-7_23","mla":"Peitz, Sebastian, et al. “Efficient Virtual Design and Testing of Autonomous Vehicles.” German Success Stories in Industrial Mathematics, edited by H. G. Bock et al., vol. 35, Springer International Publishing, 2022, doi:10.1007/978-3-030-81455-7_23.","bibtex":"@inbook{Peitz_Dellnitz_Bannenberg_2022, place={Cham}, series={Mathematics in Industry}, title={Efficient Virtual Design and Testing of Autonomous Vehicles}, volume={35}, DOI={10.1007/978-3-030-81455-7_23}, booktitle={German Success Stories in Industrial Mathematics}, publisher={Springer International Publishing}, author={Peitz, Sebastian and Dellnitz, Michael and Bannenberg, Sebastian}, editor={Bock, H. G. and Küfer, K.-H. and Maas, P. and Milde, A. and Schulz, V.}, year={2022}, collection={Mathematics in Industry} }","short":"S. Peitz, M. Dellnitz, S. Bannenberg, in: H.G. Bock, K.-H. Küfer, P. Maas, A. Milde, V. Schulz (Eds.), German Success Stories in Industrial Mathematics, Springer International Publishing, Cham, 2022.","ieee":"S. Peitz, M. Dellnitz, and S. Bannenberg, “Efficient Virtual Design and Testing of Autonomous Vehicles,” in German Success Stories in Industrial Mathematics, vol. 35, H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, and V. Schulz, Eds. Cham: Springer International Publishing, 2022."},"abstract":[{"lang":"eng","text":"With the ever increasing capabilities of sensors and controllers, autonomous driving is quickly becoming a reality. This disruptive change in the automotive industry poses major challenges for manufacturers as well as suppliers as entirely new design and testing strategies have to be developed to remain competitive. Most importantly, the complexity of autonomously driving vehicles in a complex, uncertain, and safety-critical environment requires new testing procedures to cover the almost infinite range of potential scenarios."}],"user_id":"47427","publication":"German Success Stories in Industrial Mathematics","publisher":"Springer International Publishing","author":[{"last_name":"Peitz","id":"47427","first_name":"Sebastian","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian"},{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"},{"last_name":"Bannenberg","full_name":"Bannenberg, Sebastian","first_name":"Sebastian"}],"volume":35,"date_created":"2022-03-14T07:32:41Z","status":"public","date_updated":"2022-03-14T07:42:01Z","doi":"10.1007/978-3-030-81455-7_23","series_title":"Mathematics in Industry","language":[{"iso":"eng"}],"place":"Cham","title":"Efficient Virtual Design and Testing of Autonomous Vehicles","department":[{"_id":"101"},{"_id":"655"}],"publication_identifier":{"issn":["1612-3956","2198-3283"],"isbn":["9783030814540","9783030814557"]},"publication_status":"published","editor":[{"last_name":"Bock","full_name":"Bock, H. G.","first_name":"H. G."},{"last_name":"Küfer","full_name":"Küfer, K.-H.","first_name":"K.-H."},{"last_name":"Maas","full_name":"Maas, P.","first_name":"P."},{"full_name":"Milde, A.","first_name":"A.","last_name":"Milde"},{"last_name":"Schulz","full_name":"Schulz, V.","first_name":"V."}]},{"_id":"16544","date_updated":"2022-01-06T06:52:52Z","doi":"10.1007/978-94-011-0956-7_9","language":[{"iso":"eng"}],"type":"book_chapter","year":"1994","citation":{"ieee":"M. Dellnitz and J. Scheurle, “Eigenvalue Movement for a Class of Reversible Hamiltonian Systems with Three Degrees of Freedom,” in Dynamics, Bifurcation and Symmetry, Dordrecht, 1994.","short":"M. Dellnitz, J. Scheurle, in: Dynamics, Bifurcation and Symmetry, Dordrecht, 1994.","mla":"Dellnitz, Michael, and Jürgen Scheurle. “Eigenvalue Movement for a Class of Reversible Hamiltonian Systems with Three Degrees of Freedom.” Dynamics, Bifurcation and Symmetry, 1994, doi:10.1007/978-94-011-0956-7_9.","bibtex":"@inbook{Dellnitz_Scheurle_1994, place={Dordrecht}, title={Eigenvalue Movement for a Class of Reversible Hamiltonian Systems with Three Degrees of Freedom}, DOI={10.1007/978-94-011-0956-7_9}, booktitle={Dynamics, Bifurcation and Symmetry}, author={Dellnitz, Michael and Scheurle, Jürgen}, year={1994} }","ama":"Dellnitz M, Scheurle J. Eigenvalue Movement for a Class of Reversible Hamiltonian Systems with Three Degrees of Freedom. In: Dynamics, Bifurcation and Symmetry. Dordrecht; 1994. doi:10.1007/978-94-011-0956-7_9","apa":"Dellnitz, M., & Scheurle, J. (1994). Eigenvalue Movement for a Class of Reversible Hamiltonian Systems with Three Degrees of Freedom. In Dynamics, Bifurcation and Symmetry. Dordrecht. https://doi.org/10.1007/978-94-011-0956-7_9","chicago":"Dellnitz, Michael, and Jürgen Scheurle. “Eigenvalue Movement for a Class of Reversible Hamiltonian Systems with Three Degrees of Freedom.” In Dynamics, Bifurcation and Symmetry. Dordrecht, 1994. https://doi.org/10.1007/978-94-011-0956-7_9."},"place":"Dordrecht","user_id":"15701","title":"Eigenvalue Movement for a Class of Reversible Hamiltonian Systems with Three Degrees of Freedom","publication":"Dynamics, Bifurcation and Symmetry","department":[{"_id":"101"}],"author":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"first_name":"Jürgen","full_name":"Scheurle, Jürgen","last_name":"Scheurle"}],"date_created":"2020-04-15T08:53:18Z","status":"public","publication_status":"published","publication_identifier":{"isbn":["9789401044134","9789401109567"]}},{"publication":"Cognitive Neurodynamics","department":[{"_id":"101"}],"author":[{"full_name":"Goelz, Christian","first_name":"Christian","last_name":"Goelz"},{"last_name":"Mora","full_name":"Mora, Karin","first_name":"Karin"},{"first_name":"Julia Kristin","full_name":"Stroehlein, Julia Kristin","last_name":"Stroehlein"},{"full_name":"Haase, Franziska Katharina","first_name":"Franziska Katharina","last_name":"Haase"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"last_name":"Reinsberger","full_name":"Reinsberger, Claus","first_name":"Claus"},{"last_name":"Vieluf","first_name":"Solveig","full_name":"Vieluf, Solveig"}],"date_created":"2021-02-08T13:16:07Z","status":"public","user_id":"32643","title":"Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s11571-020-09656-9.pdf"}],"language":[{"iso":"eng"}],"year":"2021","type":"journal_article","citation":{"apa":"Goelz, C., Mora, K., Stroehlein, J. K., Haase, F. K., Dellnitz, M., Reinsberger, C., & Vieluf, S. (2021). Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults. Cognitive Neurodynamics. https://doi.org/10.1007/s11571-020-09656-9","ama":"Goelz C, Mora K, Stroehlein JK, et al. Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults. Cognitive Neurodynamics. 2021. doi:10.1007/s11571-020-09656-9","chicago":"Goelz, Christian, Karin Mora, Julia Kristin Stroehlein, Franziska Katharina Haase, Michael Dellnitz, Claus Reinsberger, and Solveig Vieluf. “Electrophysiological Signatures of Dedifferentiation Differ between Fit and Less Fit Older Adults.” Cognitive Neurodynamics, 2021. https://doi.org/10.1007/s11571-020-09656-9.","bibtex":"@article{Goelz_Mora_Stroehlein_Haase_Dellnitz_Reinsberger_Vieluf_2021, title={Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults}, DOI={10.1007/s11571-020-09656-9}, journal={Cognitive Neurodynamics}, author={Goelz, Christian and Mora, Karin and Stroehlein, Julia Kristin and Haase, Franziska Katharina and Dellnitz, Michael and Reinsberger, Claus and Vieluf, Solveig}, year={2021} }","mla":"Goelz, Christian, et al. “Electrophysiological Signatures of Dedifferentiation Differ between Fit and Less Fit Older Adults.” Cognitive Neurodynamics, 2021, doi:10.1007/s11571-020-09656-9.","short":"C. Goelz, K. Mora, J.K. Stroehlein, F.K. Haase, M. Dellnitz, C. Reinsberger, S. Vieluf, Cognitive Neurodynamics (2021).","ieee":"C. Goelz et al., “Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults,” Cognitive Neurodynamics, 2021."},"_id":"21195","date_updated":"2022-01-06T06:54:49Z","doi":"10.1007/s11571-020-09656-9"},{"user_id":"15701","title":"Energy efficient control for mechanical systems based on inherent dynamical structures","department":[{"_id":"101"}],"publication":"2012 American Control Conference (ACC)","author":[{"last_name":"Flaskamp","full_name":"Flaskamp, K.","first_name":"K."},{"last_name":"Ober-Blobaum","full_name":"Ober-Blobaum, S.","first_name":"S."}],"date_created":"2020-04-16T05:49:41Z","status":"public","publication_identifier":{"isbn":["9781457710964","9781457710957","9781457710940","9781467321020"]},"publication_status":"published","_id":"16589","date_updated":"2022-01-06T06:52:52Z","doi":"10.1109/acc.2012.6314820","language":[{"iso":"eng"}],"citation":{"chicago":"Flaskamp, K., and S. Ober-Blobaum. “Energy Efficient Control for Mechanical Systems Based on Inherent Dynamical Structures.” In 2012 American Control Conference (ACC), 2012. https://doi.org/10.1109/acc.2012.6314820.","ama":"Flaskamp K, Ober-Blobaum S. Energy efficient control for mechanical systems based on inherent dynamical structures. In: 2012 American Control Conference (ACC). ; 2012. doi:10.1109/acc.2012.6314820","apa":"Flaskamp, K., & Ober-Blobaum, S. (2012). Energy efficient control for mechanical systems based on inherent dynamical structures. In 2012 American Control Conference (ACC). https://doi.org/10.1109/acc.2012.6314820","bibtex":"@inproceedings{Flaskamp_Ober-Blobaum_2012, title={Energy efficient control for mechanical systems based on inherent dynamical structures}, DOI={10.1109/acc.2012.6314820}, booktitle={2012 American Control Conference (ACC)}, author={Flaskamp, K. and Ober-Blobaum, S.}, year={2012} }","mla":"Flaskamp, K., and S. Ober-Blobaum. “Energy Efficient Control for Mechanical Systems Based on Inherent Dynamical Structures.” 2012 American Control Conference (ACC), 2012, doi:10.1109/acc.2012.6314820.","short":"K. Flaskamp, S. Ober-Blobaum, in: 2012 American Control Conference (ACC), 2012.","ieee":"K. Flaskamp and S. Ober-Blobaum, “Energy efficient control for mechanical systems based on inherent dynamical structures,” in 2012 American Control Conference (ACC), 2012."},"year":"2012","type":"conference"},{"publication_status":"published","publication_identifier":{"isbn":["1424403901","142440391X"],"issn":["1553-572X"]},"status":"public","date_created":"2020-04-16T08:20:27Z","author":[{"last_name":"Knoke","full_name":"Knoke, Tobias","first_name":"Tobias"},{"full_name":"Romaus, Christoph","first_name":"Christoph","last_name":"Romaus"},{"first_name":"Joachim","full_name":"Bocker, Joachim","last_name":"Bocker"},{"last_name":"Dell'Aere","first_name":"Alessandro","full_name":"Dell'Aere, Alessandro"},{"last_name":"Witting","full_name":"Witting, Katrin","first_name":"Katrin"}],"department":[{"_id":"101"}],"publication":"IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics","title":"Energy Management for an Onboard Storage System Based on Multi-Objective Optimization","user_id":"15701","type":"conference","citation":{"ama":"Knoke T, Romaus C, Bocker J, Dell’Aere A, Witting K. Energy Management for an Onboard Storage System Based on Multi-Objective Optimization. In: IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics. ; 2006. doi:10.1109/iecon.2006.347705","apa":"Knoke, T., Romaus, C., Bocker, J., Dell’Aere, A., & Witting, K. (2006). Energy Management for an Onboard Storage System Based on Multi-Objective Optimization. In IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics. https://doi.org/10.1109/iecon.2006.347705","chicago":"Knoke, Tobias, Christoph Romaus, Joachim Bocker, Alessandro Dell’Aere, and Katrin Witting. “Energy Management for an Onboard Storage System Based on Multi-Objective Optimization.” In IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics, 2006. https://doi.org/10.1109/iecon.2006.347705.","bibtex":"@inproceedings{Knoke_Romaus_Bocker_Dell’Aere_Witting_2006, title={Energy Management for an Onboard Storage System Based on Multi-Objective Optimization}, DOI={10.1109/iecon.2006.347705}, booktitle={IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics}, author={Knoke, Tobias and Romaus, Christoph and Bocker, Joachim and Dell’Aere, Alessandro and Witting, Katrin}, year={2006} }","mla":"Knoke, Tobias, et al. “Energy Management for an Onboard Storage System Based on Multi-Objective Optimization.” IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics, 2006, doi:10.1109/iecon.2006.347705.","short":"T. Knoke, C. Romaus, J. Bocker, A. Dell’Aere, K. Witting, in: IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics, 2006.","ieee":"T. Knoke, C. Romaus, J. Bocker, A. Dell’Aere, and K. Witting, “Energy Management for an Onboard Storage System Based on Multi-Objective Optimization,” in IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics, 2006."},"year":"2006","language":[{"iso":"eng"}],"doi":"10.1109/iecon.2006.347705","date_updated":"2022-01-06T06:52:53Z","_id":"16626"},{"title":"Energy transfer via linear doubly-fed motor in different operating modes","user_id":"15701","publication_identifier":{"isbn":["9781424442515"]},"publication_status":"published","status":"public","date_created":"2020-04-16T09:56:21Z","author":[{"last_name":"Schneider","full_name":"Schneider, T.","first_name":"T."},{"last_name":"Schulz","first_name":"B.","full_name":"Schulz, B."},{"first_name":"C.","full_name":"Henke, C.","last_name":"Henke"},{"last_name":"Witting","first_name":"K.","full_name":"Witting, K."},{"first_name":"D.","full_name":"Steenken, D.","last_name":"Steenken"},{"last_name":"Bocker","full_name":"Bocker, J.","first_name":"J."}],"department":[{"_id":"101"}],"publication":"2009 IEEE International Electric Machines and Drives Conference","doi":"10.1109/iemdc.2009.5075267","_id":"16663","date_updated":"2022-01-06T06:52:54Z","type":"conference","year":"2009","citation":{"ieee":"T. Schneider, B. Schulz, C. Henke, K. Witting, D. Steenken, and J. Bocker, “Energy transfer via linear doubly-fed motor in different operating modes,” in 2009 IEEE International Electric Machines and Drives Conference, 2009.","short":"T. Schneider, B. Schulz, C. Henke, K. Witting, D. Steenken, J. Bocker, in: 2009 IEEE International Electric Machines and Drives Conference, 2009.","bibtex":"@inproceedings{Schneider_Schulz_Henke_Witting_Steenken_Bocker_2009, title={Energy transfer via linear doubly-fed motor in different operating modes}, DOI={10.1109/iemdc.2009.5075267}, booktitle={2009 IEEE International Electric Machines and Drives Conference}, author={Schneider, T. and Schulz, B. and Henke, C. and Witting, K. and Steenken, D. and Bocker, J.}, year={2009} }","mla":"Schneider, T., et al. “Energy Transfer via Linear Doubly-Fed Motor in Different Operating Modes.” 2009 IEEE International Electric Machines and Drives Conference, 2009, doi:10.1109/iemdc.2009.5075267.","chicago":"Schneider, T., B. Schulz, C. Henke, K. Witting, D. Steenken, and J. Bocker. “Energy Transfer via Linear Doubly-Fed Motor in Different Operating Modes.” In 2009 IEEE International Electric Machines and Drives Conference, 2009. https://doi.org/10.1109/iemdc.2009.5075267.","apa":"Schneider, T., Schulz, B., Henke, C., Witting, K., Steenken, D., & Bocker, J. (2009). Energy transfer via linear doubly-fed motor in different operating modes. In 2009 IEEE International Electric Machines and Drives Conference. https://doi.org/10.1109/iemdc.2009.5075267","ama":"Schneider T, Schulz B, Henke C, Witting K, Steenken D, Bocker J. Energy transfer via linear doubly-fed motor in different operating modes. In: 2009 IEEE International Electric Machines and Drives Conference. ; 2009. doi:10.1109/iemdc.2009.5075267"}},{"abstract":[{"lang":"eng","text":"In real-world problems, uncertainties (e.g., errors in the measurement,\r\nprecision errors) often lead to poor performance of numerical algorithms when\r\nnot explicitly taken into account. This is also the case for control problems,\r\nwhere optimal solutions can degrade in quality or even become infeasible. Thus,\r\nthere is the need to design methods that can handle uncertainty. In this work,\r\nwe consider nonlinear multi-objective optimal control problems with uncertainty\r\non the initial conditions, and in particular their incorporation into a\r\nfeedback loop via model predictive control (MPC). In multi-objective optimal\r\ncontrol, an optimal compromise between multiple conflicting criteria has to be\r\nfound. For such problems, not much has been reported in terms of uncertainties.\r\nTo address this problem class, we design an offline/online framework to compute\r\nan approximation of efficient control strategies. This approach is closely\r\nrelated to explicit MPC for nonlinear systems, where the potentially expensive\r\noptimization problem is solved in an offline phase in order to enable fast\r\nsolutions in the online phase. In order to reduce the numerical cost of the\r\noffline phase, we exploit symmetries in the control problems. Furthermore, in\r\norder to ensure optimality of the solutions, we include an additional online\r\noptimization step, which is considerably cheaper than the original\r\nmulti-objective optimization problem. We test our framework on a car\r\nmaneuvering problem where safety and speed are the objectives. The\r\nmulti-objective framework allows for online adaptations of the desired\r\nobjective. Alternatively, an automatic scalarizing procedure yields very\r\nefficient feedback controls. Our results show that the method is capable of\r\ndesigning driving strategies that deal better with uncertainties in the initial\r\nconditions, which translates into potentially safer and faster driving\r\nstrategies."}],"title":"Explicit Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty","user_id":"15694","publication":"International Journal of Robust and Nonlinear Control","department":[{"_id":"101"}],"author":[{"first_name":"Carlos Ignacio","full_name":"Hernández Castellanos, Carlos Ignacio","last_name":"Hernández Castellanos"},{"id":"16494","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"},{"last_name":"Peitz","id":"47427","first_name":"Sebastian","full_name":"Peitz, Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X"}],"volume":"30(17)","date_created":"2020-03-13T12:45:56Z","status":"public","_id":"16297","date_updated":"2022-01-21T09:55:39Z","doi":"10.1002/rnc.5197","page":"7593-7618","citation":{"ieee":"C. I. Hernández Castellanos, S. Ober-Blöbaum, and S. Peitz, “Explicit Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty,” International Journal of Robust and Nonlinear Control, vol. 30(17), pp. 7593–7618, 2020, doi: 10.1002/rnc.5197.","short":"C.I. Hernández Castellanos, S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear Control 30(17) (2020) 7593–7618.","mla":"Hernández Castellanos, Carlos Ignacio, et al. “Explicit Multi-Objective Model Predictive Control for Nonlinear Systems Under Uncertainty.” International Journal of Robust and Nonlinear Control, vol. 30(17), 2020, pp. 7593–618, doi:10.1002/rnc.5197.","bibtex":"@article{Hernández Castellanos_Ober-Blöbaum_Peitz_2020, title={Explicit Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty}, volume={30(17)}, DOI={10.1002/rnc.5197}, journal={International Journal of Robust and Nonlinear Control}, author={Hernández Castellanos, Carlos Ignacio and Ober-Blöbaum, Sina and Peitz, Sebastian}, year={2020}, pages={7593–7618} }","chicago":"Hernández Castellanos, Carlos Ignacio, Sina Ober-Blöbaum, and Sebastian Peitz. “Explicit Multi-Objective Model Predictive Control for Nonlinear Systems Under Uncertainty.” International Journal of Robust and Nonlinear Control 30(17) (2020): 7593–7618. https://doi.org/10.1002/rnc.5197.","ama":"Hernández Castellanos CI, Ober-Blöbaum S, Peitz S. Explicit Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty. International Journal of Robust and Nonlinear Control. 2020;30(17):7593-7618. doi:10.1002/rnc.5197","apa":"Hernández Castellanos, C. I., Ober-Blöbaum, S., & Peitz, S. (2020). Explicit Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty. International Journal of Robust and Nonlinear Control, 30(17), 7593–7618. https://doi.org/10.1002/rnc.5197"},"year":"2020","type":"journal_article","language":[{"iso":"eng"}]},{"oa":"1","doi":"10.1002/rnc.5281","_id":"16294","date_updated":"2022-01-24T13:27:50Z","language":[{"iso":"eng"}],"page":"380-403","citation":{"ieee":"S. Ober-Blöbaum and S. Peitz, “Explicit multiobjective model predictive control for nonlinear systems with symmetries,” International Journal of Robust and Nonlinear Control, vol. 31(2), pp. 380–403, 2021, doi: 10.1002/rnc.5281.","short":"S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear Control 31(2) (2021) 380–403.","bibtex":"@article{Ober-Blöbaum_Peitz_2021, title={Explicit multiobjective model predictive control for nonlinear systems with symmetries}, volume={31(2)}, DOI={10.1002/rnc.5281}, journal={International Journal of Robust and Nonlinear Control}, author={Ober-Blöbaum, Sina and Peitz, Sebastian}, year={2021}, pages={380–403} }","mla":"Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems with Symmetries.” International Journal of Robust and Nonlinear Control, vol. 31(2), 2021, pp. 380–403, doi:10.1002/rnc.5281.","chicago":"Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems with Symmetries.” International Journal of Robust and Nonlinear Control 31(2) (2021): 380–403. https://doi.org/10.1002/rnc.5281.","ama":"Ober-Blöbaum S, Peitz S. Explicit multiobjective model predictive control for nonlinear systems with symmetries. International Journal of Robust and Nonlinear Control. 2021;31(2):380-403. doi:10.1002/rnc.5281","apa":"Ober-Blöbaum, S., & Peitz, S. (2021). Explicit multiobjective model predictive control for nonlinear systems with symmetries. International Journal of Robust and Nonlinear Control, 31(2), 380–403. https://doi.org/10.1002/rnc.5281"},"year":"2021","type":"journal_article","main_file_link":[{"url":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/rnc.5281","open_access":"1"}],"user_id":"15694","title":"Explicit multiobjective model predictive control for nonlinear systems with symmetries","abstract":[{"lang":"eng","text":"Model predictive control is a prominent approach to construct a feedback\r\ncontrol loop for dynamical systems. Due to real-time constraints, the major\r\nchallenge in MPC is to solve model-based optimal control problems in a very\r\nshort amount of time. For linear-quadratic problems, Bemporad et al. have\r\nproposed an explicit formulation where the underlying optimization problems are\r\nsolved a priori in an offline phase. In this article, we present an extension\r\nof this concept in two significant ways. We consider nonlinear problems and -\r\nmore importantly - problems with multiple conflicting objective functions. In\r\nthe offline phase, we build a library of Pareto optimal solutions from which we\r\nthen obtain a valid compromise solution in the online phase according to a\r\ndecision maker's preference. Since the standard multi-parametric programming\r\napproach is no longer valid in this situation, we instead use interpolation\r\nbetween different entries of the library. To reduce the number of problems that\r\nhave to be solved in the offline phase, we exploit symmetries in the dynamical\r\nsystem and the corresponding multiobjective optimal control problem. The\r\nresults are verified using two different examples from autonomous driving."}],"project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"date_created":"2020-03-13T12:44:36Z","status":"public","volume":"31(2)","department":[{"_id":"101"}],"publication":"International Journal of Robust and Nonlinear Control","author":[{"last_name":"Ober-Blöbaum","id":"16494","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","id":"47427"}]},{"author":[{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"},{"first_name":"Andreas","full_name":"Hohmann, Andreas","last_name":"Hohmann"},{"full_name":"Junge, Oliver","first_name":"Oliver","last_name":"Junge"},{"last_name":"Rumpf","full_name":"Rumpf, Martin","first_name":"Martin"}],"publication":"Chaos: An Interdisciplinary Journal of Nonlinear Science","department":[{"_id":"101"}],"status":"public","date_created":"2020-04-15T09:06:28Z","publication_identifier":{"issn":["1054-1500","1089-7682"]},"publication_status":"published","user_id":"15701","title":"Exploring invariant sets and invariant measures","language":[{"iso":"eng"}],"citation":{"short":"M. Dellnitz, A. Hohmann, O. Junge, M. Rumpf, Chaos: An Interdisciplinary Journal of Nonlinear Science (1997) 221–228.","ieee":"M. Dellnitz, A. Hohmann, O. Junge, and M. Rumpf, “Exploring invariant sets and invariant measures,” Chaos: An Interdisciplinary Journal of Nonlinear Science, pp. 221–228, 1997.","ama":"Dellnitz M, Hohmann A, Junge O, Rumpf M. Exploring invariant sets and invariant measures. Chaos: An Interdisciplinary Journal of Nonlinear Science. 1997:221-228. doi:10.1063/1.166223","apa":"Dellnitz, M., Hohmann, A., Junge, O., & Rumpf, M. (1997). Exploring invariant sets and invariant measures. Chaos: An Interdisciplinary Journal of Nonlinear Science, 221–228. https://doi.org/10.1063/1.166223","chicago":"Dellnitz, Michael, Andreas Hohmann, Oliver Junge, and Martin Rumpf. “Exploring Invariant Sets and Invariant Measures.” Chaos: An Interdisciplinary Journal of Nonlinear Science, 1997, 221–28. https://doi.org/10.1063/1.166223.","bibtex":"@article{Dellnitz_Hohmann_Junge_Rumpf_1997, title={Exploring invariant sets and invariant measures}, DOI={10.1063/1.166223}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, author={Dellnitz, Michael and Hohmann, Andreas and Junge, Oliver and Rumpf, Martin}, year={1997}, pages={221–228} }","mla":"Dellnitz, Michael, et al. “Exploring Invariant Sets and Invariant Measures.” Chaos: An Interdisciplinary Journal of Nonlinear Science, 1997, pp. 221–28, doi:10.1063/1.166223."},"type":"journal_article","year":"1997","page":"221-228","_id":"16552","date_updated":"2022-01-06T06:52:52Z","doi":"10.1063/1.166223"},{"year":"2001","citation":{"short":"G. Froyland, in: Nonlinear Dynamics and Statistics, Boston, MA, 2001.","ieee":"G. Froyland, “Extracting Dynamical Behavior via Markov Models,” in Nonlinear Dynamics and Statistics, Boston, MA, 2001.","chicago":"Froyland, Gary. “Extracting Dynamical Behavior via Markov Models.” In Nonlinear Dynamics and Statistics. Boston, MA, 2001. https://doi.org/10.1007/978-1-4612-0177-9_12.","apa":"Froyland, G. (2001). Extracting Dynamical Behavior via Markov Models. In Nonlinear Dynamics and Statistics. Boston, MA. https://doi.org/10.1007/978-1-4612-0177-9_12","ama":"Froyland G. Extracting Dynamical Behavior via Markov Models. In: Nonlinear Dynamics and Statistics. Boston, MA; 2001. doi:10.1007/978-1-4612-0177-9_12","mla":"Froyland, Gary. “Extracting Dynamical Behavior via Markov Models.” Nonlinear Dynamics and Statistics, 2001, doi:10.1007/978-1-4612-0177-9_12.","bibtex":"@inbook{Froyland_2001, place={Boston, MA}, title={Extracting Dynamical Behavior via Markov Models}, DOI={10.1007/978-1-4612-0177-9_12}, booktitle={Nonlinear Dynamics and Statistics}, author={Froyland, Gary}, year={2001} }"},"type":"book_chapter","language":[{"iso":"eng"}],"doi":"10.1007/978-1-4612-0177-9_12","_id":"16598","date_updated":"2022-01-06T06:52:52Z","publication_identifier":{"isbn":["9781461266488","9781461201779"]},"publication_status":"published","date_created":"2020-04-16T06:03:45Z","status":"public","publication":"Nonlinear Dynamics and Statistics","department":[{"_id":"101"}],"author":[{"last_name":"Froyland","first_name":"Gary","full_name":"Froyland, Gary"}],"title":"Extracting Dynamical Behavior via Markov Models","user_id":"15701","place":"Boston, MA"},{"status":"public","date_created":"2022-07-28T11:53:02Z","author":[{"first_name":"Konstantin","orcid":"https://orcid.org/0000-0003-3384-3496","full_name":"Sonntag, Konstantin","last_name":"Sonntag","id":"56399"},{"id":"47427","last_name":"Peitz","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian"}],"publication":"arXiv:2307.00975","department":[{"_id":"101"},{"_id":"655"}],"title":"Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping","user_id":"56399","abstract":[{"lang":"eng","text":"We present a new gradient-like dynamical system related to unconstrained convex smooth multiobjective optimization which involves inertial effects and asymptotic vanishing damping. To the best of our knowledge, this system is the first inertial gradient-like system for multiobjective optimization problems including asymptotic vanishing damping, expanding the ideas laid out in [H. Attouch and G. Garrigos, Multiobjective optimization: an inertial approach to Pareto optima, preprint, arXiv:1506.02823, 201]. We prove existence of solutions to this system in finite dimensions and further prove that its bounded solutions converge weakly to weakly Pareto optimal points. In addition, we obtain a convergence rate of order O(t−2) for the function values measured with a merit function. This approach presents a good basis for the development of fast gradient methods for multiobjective optimization."}],"external_id":{"arxiv":["2307.00975"]},"citation":{"chicago":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping.” ArXiv:2307.00975, 2023.","ama":"Sonntag K, Peitz S. Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping. arXiv:230700975. Published online 2023.","apa":"Sonntag, K., & Peitz, S. (2023). Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping. In arXiv:2307.00975.","mla":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping.” ArXiv:2307.00975, 2023.","bibtex":"@article{Sonntag_Peitz_2023, title={Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping}, journal={arXiv:2307.00975}, author={Sonntag, Konstantin and Peitz, Sebastian}, year={2023} }","short":"K. Sonntag, S. Peitz, ArXiv:2307.00975 (2023).","ieee":"K. Sonntag and S. Peitz, “Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping,” arXiv:2307.00975. 2023."},"type":"preprint","year":"2023","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2307.00975.pdf"}],"oa":"1","date_updated":"2024-02-21T10:15:33Z","_id":"32447"},{"date_created":"2023-07-12T06:35:58Z","status":"public","publication_status":"published","department":[{"_id":"101"},{"_id":"655"}],"publication":"Journal of Optimization Theory and Applications","author":[{"id":"56399","last_name":"Sonntag","full_name":"Sonntag, Konstantin","orcid":"https://orcid.org/0000-0003-3384-3496","first_name":"Konstantin"},{"last_name":"Peitz","id":"47427","first_name":"Sebastian","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X"}],"publisher":"Springer","user_id":"56399","title":"Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems","abstract":[{"lang":"eng","text":"We derive efficient algorithms to compute weakly Pareto optimal solutions for smooth, convex and unconstrained multiobjective optimization problems in general Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical system in the multiobjective setting, which trajectories converge weakly to Pareto optimal solutions. Discretization of this system yields an inertial multiobjective algorithm which generates sequences that converge weakly to Pareto optimal solutions. We employ Nesterov acceleration to define an algorithm with an improved convergence rate compared to the plain multiobjective steepest descent method (Algorithm 1). A further improvement in terms of efficiency is achieved by avoiding the solution of a quadratic subproblem to compute a common step direction for all objective functions, which is usually required in first-order methods. Using a different discretization of our inertial gradient-like dynamical system, we obtain an accelerated multiobjective gradient method that does not require the solution of a subproblem in each step (Algorithm 2). While this algorithm does not converge in general, it yields good results on test problems while being faster than standard steepest descent."}],"language":[{"iso":"eng"}],"citation":{"short":"K. Sonntag, S. Peitz, Journal of Optimization Theory and Applications (2024).","ieee":"K. Sonntag and S. Peitz, “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems,” Journal of Optimization Theory and Applications, 2024, doi: 10.1007/s10957-024-02389-3.","ama":"Sonntag K, Peitz S. Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems. Journal of Optimization Theory and Applications. Published online 2024. doi:10.1007/s10957-024-02389-3","apa":"Sonntag, K., & Peitz, S. (2024). Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems. Journal of Optimization Theory and Applications. https://doi.org/10.1007/s10957-024-02389-3","chicago":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal of Optimization Theory and Applications, 2024. https://doi.org/10.1007/s10957-024-02389-3.","bibtex":"@article{Sonntag_Peitz_2024, title={Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems}, DOI={10.1007/s10957-024-02389-3}, journal={Journal of Optimization Theory and Applications}, publisher={Springer}, author={Sonntag, Konstantin and Peitz, Sebastian}, year={2024} }","mla":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal of Optimization Theory and Applications, Springer, 2024, doi:10.1007/s10957-024-02389-3."},"type":"journal_article","year":"2024","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10957-024-02389-3.pdf","open_access":"1"}],"oa":"1","doi":"10.1007/s10957-024-02389-3","_id":"46019","date_updated":"2024-02-21T10:13:33Z"},{"language":[{"iso":"eng"}],"series_title":"Lecture Notes in Control and Information Sciences","doi":"10.1007/978-3-030-35713-9_10","date_updated":"2022-01-06T06:52:48Z","publication_identifier":{"issn":["0170-8643","1610-7411"],"isbn":["9783030357122","9783030357139"]},"publication_status":"published","department":[{"_id":"101"}],"title":"Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator","place":"Cham","page":"257-282","type":"book_chapter","citation":{"short":"S. Peitz, S. Klus, in: Lecture Notes in Control and Information Sciences, Springer, Cham, 2020, pp. 257–282.","ieee":"S. Peitz and S. Klus, “Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator,” in Lecture Notes in Control and Information Sciences, vol. 484, Cham: Springer, 2020, pp. 257–282.","chicago":"Peitz, Sebastian, and Stefan Klus. “Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator.” In Lecture Notes in Control and Information Sciences, 484:257–82. Lecture Notes in Control and Information Sciences. Cham: Springer, 2020. https://doi.org/10.1007/978-3-030-35713-9_10.","ama":"Peitz S, Klus S. Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator. In: Lecture Notes in Control and Information Sciences. Vol 484. Lecture Notes in Control and Information Sciences. Cham: Springer; 2020:257-282. doi:10.1007/978-3-030-35713-9_10","apa":"Peitz, S., & Klus, S. (2020). Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator. In Lecture Notes in Control and Information Sciences (Vol. 484, pp. 257–282). Cham: Springer. https://doi.org/10.1007/978-3-030-35713-9_10","bibtex":"@inbook{Peitz_Klus_2020, place={Cham}, series={Lecture Notes in Control and Information Sciences}, title={Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator}, volume={484}, DOI={10.1007/978-3-030-35713-9_10}, booktitle={Lecture Notes in Control and Information Sciences}, publisher={Springer}, author={Peitz, Sebastian and Klus, Stefan}, year={2020}, pages={257–282}, collection={Lecture Notes in Control and Information Sciences} }","mla":"Peitz, Sebastian, and Stefan Klus. “Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator.” Lecture Notes in Control and Information Sciences, vol. 484, Springer, 2020, pp. 257–82, doi:10.1007/978-3-030-35713-9_10."},"year":"2020","_id":"16289","intvolume":" 484","volume":484,"date_created":"2020-03-13T12:38:52Z","status":"public","publication":"Lecture Notes in Control and Information Sciences","author":[{"orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian","id":"47427","last_name":"Peitz"},{"full_name":"Klus, Stefan","first_name":"Stefan","last_name":"Klus"}],"publisher":"Springer","user_id":"47427","abstract":[{"lang":"eng","text":"In the development of model predictive controllers for PDE-constrained problems, the use of reduced order models is essential to enable real-time applicability. Besides local linearization approaches, proper orthogonal decomposition (POD) has been most widely used in the past in order to derive such models. Due to the huge advances concerning both theory as well as the numerical approximation, a very promising alternative based on the Koopman operator has recently emerged. In this chapter, we present two control strategies for model predictive control of nonlinear PDEs using data-efficient approximations of the Koopman operator. In the first one, the dynamic control system is replaced by a small number of autonomous systems with different yet constant inputs. The control problem is consequently transformed into a switching problem. In the second approach, a bilinear surrogate model is obtained via a convex combination of these autonomous systems. Using a recent convergence result for extended dynamic mode decomposition (EDMD), convergence of the reduced objective function can be shown. We study the properties of these two strategies with respect to solution quality, data requirements, and complexity of the resulting optimization problem using the 1-dimensional Burgers equation and the 2-dimensional Navier–Stokes equations as examples. Finally, an extension for online adaptivity is presented."}]},{"author":[{"first_name":"M.","full_name":"Dellnitz, M.","last_name":"Dellnitz"}],"department":[{"_id":"101"}],"publication":"IMA Journal of Numerical Analysis","status":"public","date_created":"2020-04-15T09:12:17Z","publication_status":"published","publication_identifier":{"issn":["0272-4979","1464-3642"]},"user_id":"15701","title":"Finding zeros by multilevel subdivision techniques","language":[{"iso":"eng"}],"year":"2002","citation":{"mla":"Dellnitz, M. “Finding Zeros by Multilevel Subdivision Techniques.” IMA Journal of Numerical Analysis, 2002, pp. 167–85, doi:10.1093/imanum/22.2.167.","bibtex":"@article{Dellnitz_2002, title={Finding zeros by multilevel subdivision techniques}, DOI={10.1093/imanum/22.2.167}, journal={IMA Journal of Numerical Analysis}, author={Dellnitz, M.}, year={2002}, pages={167–185} }","chicago":"Dellnitz, M. “Finding Zeros by Multilevel Subdivision Techniques.” IMA Journal of Numerical Analysis, 2002, 167–85. https://doi.org/10.1093/imanum/22.2.167.","apa":"Dellnitz, M. (2002). Finding zeros by multilevel subdivision techniques. IMA Journal of Numerical Analysis, 167–185. https://doi.org/10.1093/imanum/22.2.167","ama":"Dellnitz M. Finding zeros by multilevel subdivision techniques. IMA Journal of Numerical Analysis. 2002:167-185. doi:10.1093/imanum/22.2.167","ieee":"M. Dellnitz, “Finding zeros by multilevel subdivision techniques,” IMA Journal of Numerical Analysis, pp. 167–185, 2002.","short":"M. Dellnitz, IMA Journal of Numerical Analysis (2002) 167–185."},"type":"journal_article","page":"167-185","_id":"16556","date_updated":"2022-01-06T06:52:52Z","doi":"10.1093/imanum/22.2.167"},{"language":[{"iso":"eng"}],"year":"2019","citation":{"ieee":"S. Hanke, S. Peitz, O. Wallscheid, J. Böcker, and M. Dellnitz, “Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification,” in 2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE), 2019.","short":"S. Hanke, S. Peitz, O. Wallscheid, J. Böcker, M. Dellnitz, in: 2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE), 2019.","mla":"Hanke, Soren, et al. “Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification.” 2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE), 2019, doi:10.1109/precede.2019.8753313.","bibtex":"@inproceedings{Hanke_Peitz_Wallscheid_Böcker_Dellnitz_2019, title={Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification}, DOI={10.1109/precede.2019.8753313}, booktitle={2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)}, author={Hanke, Soren and Peitz, Sebastian and Wallscheid, Oliver and Böcker, Joachim and Dellnitz, Michael}, year={2019} }","chicago":"Hanke, Soren, Sebastian Peitz, Oliver Wallscheid, Joachim Böcker, and Michael Dellnitz. “Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification.” In 2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE), 2019. https://doi.org/10.1109/precede.2019.8753313.","ama":"Hanke S, Peitz S, Wallscheid O, Böcker J, Dellnitz M. Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification. In: 2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE). ; 2019. doi:10.1109/precede.2019.8753313","apa":"Hanke, S., Peitz, S., Wallscheid, O., Böcker, J., & Dellnitz, M. (2019). Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification. In 2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE). https://doi.org/10.1109/precede.2019.8753313"},"type":"conference","doi":"10.1109/precede.2019.8753313","date_updated":"2022-01-06T06:50:46Z","_id":"10597","date_created":"2019-07-10T08:15:23Z","status":"public","publication_identifier":{"isbn":["9781538694145"]},"publication_status":"published","publication":"2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)","department":[{"_id":"101"}],"author":[{"last_name":"Hanke","full_name":"Hanke, Soren","first_name":"Soren"},{"orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian","id":"47427","last_name":"Peitz"},{"last_name":"Wallscheid","full_name":"Wallscheid, Oliver","first_name":"Oliver"},{"last_name":"Böcker","first_name":"Joachim","full_name":"Böcker, Joachim"},{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"}],"user_id":"47427","title":"Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification","abstract":[{"text":"In comparison to classical control approaches in the field of electrical drives like the field-oriented control (FOC), model predictive control (MPC) approaches are able to provide a higher control performance. This refers to shorter settling times, lower overshoots, and a better decoupling of control variables in case of multi-variable controls. However, this can only be achieved if the used prediction model covers the actual behavior of the plant sufficiently well. In case of model deviations, the performance utilizing MPC remains below its potential. This results in effects like increased current ripple or steady state setpoint deviations. In order to achieve a high control performance, it is therefore necessary to adapt the model to the real plant behavior. When using an online system identification, a less accurate model is sufficient for commissioning of the drive system. In this paper, the combination of a finite-control-set MPC (FCS-MPC) with a system identification is proposed. The method does not require high-frequency signal injection, but uses the measured values already required for the FCS-MPC. An evaluation of the least squares-based identification on a laboratory test bench showed that the model accuracy and thus the control performance could be improved by an online update of the prediction models.","lang":"eng"}]},{"language":[{"iso":"eng"}],"oa":"1","doi":"10.1007/s00332-022-09862-1","date_updated":"2023-08-24T07:50:12Z","publication_status":"published","department":[{"_id":"101"},{"_id":"655"}],"title":"Finite-data error bounds for Koopman-based prediction and control","type":"journal_article","year":"2023","citation":{"ieee":"F. Nüske, S. Peitz, F. Philipp, M. Schaller, and K. Worthmann, “Finite-data error bounds for Koopman-based prediction and control,” Journal of Nonlinear Science, vol. 33, Art. no. 14, 2023, doi: 10.1007/s00332-022-09862-1.","short":"F. Nüske, S. Peitz, F. Philipp, M. Schaller, K. Worthmann, Journal of Nonlinear Science 33 (2023).","mla":"Nüske, Feliks, et al. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.” Journal of Nonlinear Science, vol. 33, 14, 2023, doi:10.1007/s00332-022-09862-1.","bibtex":"@article{Nüske_Peitz_Philipp_Schaller_Worthmann_2023, title={Finite-data error bounds for Koopman-based prediction and control}, volume={33}, DOI={10.1007/s00332-022-09862-1}, number={14}, journal={Journal of Nonlinear Science}, author={Nüske, Feliks and Peitz, Sebastian and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl}, year={2023} }","apa":"Nüske, F., Peitz, S., Philipp, F., Schaller, M., & Worthmann, K. (2023). Finite-data error bounds for Koopman-based prediction and control. Journal of Nonlinear Science, 33, Article 14. https://doi.org/10.1007/s00332-022-09862-1","ama":"Nüske F, Peitz S, Philipp F, Schaller M, Worthmann K. Finite-data error bounds for Koopman-based prediction and control. Journal of Nonlinear Science. 2023;33. doi:10.1007/s00332-022-09862-1","chicago":"Nüske, Feliks, Sebastian Peitz, Friedrich Philipp, Manuel Schaller, and Karl Worthmann. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.” Journal of Nonlinear Science 33 (2023). https://doi.org/10.1007/s00332-022-09862-1."},"main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s00332-022-09862-1.pdf"}],"article_number":"14","_id":"23428","intvolume":" 33","status":"public","date_created":"2021-08-17T12:25:09Z","volume":33,"author":[{"first_name":"Feliks","full_name":"Nüske, Feliks","orcid":"0000-0003-2444-7889","last_name":"Nüske","id":"81513"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427"},{"full_name":"Philipp, Friedrich","first_name":"Friedrich","last_name":"Philipp"},{"last_name":"Schaller","first_name":"Manuel","full_name":"Schaller, Manuel"},{"last_name":"Worthmann","full_name":"Worthmann, Karl","first_name":"Karl"}],"publication":"Journal of Nonlinear Science","user_id":"47427","abstract":[{"text":"The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems in recent years, e.g., via extended dynamic mode decomposition. Despite its popularity, convergence results and, in particular, error bounds are still quite scarce. In this paper, we derive probabilistic bounds for the approximation error and the prediction error depending on the number of training data points; for both ordinary and stochastic differential equations. Moreover, we extend our analysis to nonlinear control-affine systems using either ergodic trajectories or i.i.d.\r\nsamples. Here, we exploit the linearity of the Koopman generator to obtain a bilinear system and, thus, circumvent the curse of dimensionality since we do not autonomize the system by augmenting the state by the control inputs. To the\r\nbest of our knowledge, this is the first finite-data error analysis in the stochastic and/or control setting. Finally, we demonstrate the effectiveness of the proposed approach by comparing it with state-of-the-art techniques showing its superiority whenever state and control are coupled.","lang":"eng"}]},{"doi":"10.1088/0951-7715/5/4/008","_id":"16548","date_updated":"2022-01-06T06:52:52Z","language":[{"iso":"eng"}],"year":"1992","type":"journal_article","citation":{"short":"M. Dellnitz, I. Melbourne, J.E. Marsden, Nonlinearity (1992) 979–996.","ieee":"M. Dellnitz, I. Melbourne, and J. E. Marsden, “Generic bifurcation of Hamiltonian vector fields with symmetry,” Nonlinearity, pp. 979–996, 1992.","ama":"Dellnitz M, Melbourne I, Marsden JE. Generic bifurcation of Hamiltonian vector fields with symmetry. Nonlinearity. 1992:979-996. doi:10.1088/0951-7715/5/4/008","apa":"Dellnitz, M., Melbourne, I., & Marsden, J. E. (1992). Generic bifurcation of Hamiltonian vector fields with symmetry. Nonlinearity, 979–996. https://doi.org/10.1088/0951-7715/5/4/008","chicago":"Dellnitz, M, I Melbourne, and J E Marsden. “Generic Bifurcation of Hamiltonian Vector Fields with Symmetry.” Nonlinearity, 1992, 979–96. https://doi.org/10.1088/0951-7715/5/4/008.","bibtex":"@article{Dellnitz_Melbourne_Marsden_1992, title={Generic bifurcation of Hamiltonian vector fields with symmetry}, DOI={10.1088/0951-7715/5/4/008}, journal={Nonlinearity}, author={Dellnitz, M and Melbourne, I and Marsden, J E}, year={1992}, pages={979–996} }","mla":"Dellnitz, M., et al. “Generic Bifurcation of Hamiltonian Vector Fields with Symmetry.” Nonlinearity, 1992, pp. 979–96, doi:10.1088/0951-7715/5/4/008."},"page":"979-996","user_id":"15701","title":"Generic bifurcation of Hamiltonian vector fields with symmetry","status":"public","date_created":"2020-04-15T08:59:25Z","publication_status":"published","publication_identifier":{"issn":["0951-7715","1361-6544"]},"author":[{"last_name":"Dellnitz","full_name":"Dellnitz, M","first_name":"M"},{"full_name":"Melbourne, I","first_name":"I","last_name":"Melbourne"},{"full_name":"Marsden, J E","first_name":"J E","last_name":"Marsden"}],"publication":"Nonlinearity","department":[{"_id":"101"}]},{"department":[{"_id":"101"}],"publication":"Bifurcation and Symmetry","author":[{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"last_name":"Marsden","first_name":"Jerrold E.","full_name":"Marsden, Jerrold E."},{"first_name":"Ian","full_name":"Melbourne, Ian","last_name":"Melbourne"},{"first_name":"Jürgen","full_name":"Scheurle, Jürgen","last_name":"Scheurle"}],"publication_status":"published","publication_identifier":{"isbn":["9783034875387","9783034875363"]},"date_created":"2020-04-15T08:58:01Z","status":"public","place":"Basel","title":"Generic Bifurcations of Pendula","user_id":"15701","type":"book_chapter","year":"1992","citation":{"bibtex":"@inbook{Dellnitz_Marsden_Melbourne_Scheurle_1992, place={Basel}, title={Generic Bifurcations of Pendula}, DOI={10.1007/978-3-0348-7536-3_10}, booktitle={Bifurcation and Symmetry}, author={Dellnitz, Michael and Marsden, Jerrold E. and Melbourne, Ian and Scheurle, Jürgen}, year={1992} }","mla":"Dellnitz, Michael, et al. “Generic Bifurcations of Pendula.” Bifurcation and Symmetry, 1992, doi:10.1007/978-3-0348-7536-3_10.","chicago":"Dellnitz, Michael, Jerrold E. Marsden, Ian Melbourne, and Jürgen Scheurle. “Generic Bifurcations of Pendula.” In Bifurcation and Symmetry. Basel, 1992. https://doi.org/10.1007/978-3-0348-7536-3_10.","ama":"Dellnitz M, Marsden JE, Melbourne I, Scheurle J. Generic Bifurcations of Pendula. In: Bifurcation and Symmetry. Basel; 1992. doi:10.1007/978-3-0348-7536-3_10","apa":"Dellnitz, M., Marsden, J. E., Melbourne, I., & Scheurle, J. (1992). Generic Bifurcations of Pendula. In Bifurcation and Symmetry. Basel. https://doi.org/10.1007/978-3-0348-7536-3_10","ieee":"M. Dellnitz, J. E. Marsden, I. Melbourne, and J. Scheurle, “Generic Bifurcations of Pendula,” in Bifurcation and Symmetry, Basel, 1992.","short":"M. Dellnitz, J.E. Marsden, I. Melbourne, J. Scheurle, in: Bifurcation and Symmetry, Basel, 1992."},"language":[{"iso":"eng"}],"_id":"16547","date_updated":"2022-01-06T06:52:52Z","doi":"10.1007/978-3-0348-7536-3_10"},{"doi":"10.1016/0377-0427(94)90032-9","_id":"16541","date_updated":"2022-01-06T06:52:52Z","language":[{"iso":"eng"}],"page":"249-259","type":"journal_article","citation":{"short":"M. Dellnitz, I. Melbourne, Journal of Computational and Applied Mathematics (1994) 249–259.","ieee":"M. Dellnitz and I. Melbourne, “Generic movement of eigenvalues for equivariant self-adjoint matrices,” Journal of Computational and Applied Mathematics, pp. 249–259, 1994.","chicago":"Dellnitz, Michael, and Ian Melbourne. “Generic Movement of Eigenvalues for Equivariant Self-Adjoint Matrices.” Journal of Computational and Applied Mathematics, 1994, 249–59. https://doi.org/10.1016/0377-0427(94)90032-9.","ama":"Dellnitz M, Melbourne I. Generic movement of eigenvalues for equivariant self-adjoint matrices. Journal of Computational and Applied Mathematics. 1994:249-259. doi:10.1016/0377-0427(94)90032-9","apa":"Dellnitz, M., & Melbourne, I. (1994). Generic movement of eigenvalues for equivariant self-adjoint matrices. Journal of Computational and Applied Mathematics, 249–259. https://doi.org/10.1016/0377-0427(94)90032-9","mla":"Dellnitz, Michael, and Ian Melbourne. “Generic Movement of Eigenvalues for Equivariant Self-Adjoint Matrices.” Journal of Computational and Applied Mathematics, 1994, pp. 249–59, doi:10.1016/0377-0427(94)90032-9.","bibtex":"@article{Dellnitz_Melbourne_1994, title={Generic movement of eigenvalues for equivariant self-adjoint matrices}, DOI={10.1016/0377-0427(94)90032-9}, journal={Journal of Computational and Applied Mathematics}, author={Dellnitz, Michael and Melbourne, Ian}, year={1994}, pages={249–259} }"},"year":"1994","user_id":"15701","title":"Generic movement of eigenvalues for equivariant self-adjoint matrices","date_created":"2020-04-15T08:44:12Z","status":"public","publication_identifier":{"issn":["0377-0427"]},"publication_status":"published","department":[{"_id":"101"}],"publication":"Journal of Computational and Applied Mathematics","author":[{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"},{"last_name":"Melbourne","first_name":"Ian","full_name":"Melbourne, Ian"}]},{"language":[{"iso":"eng"}],"year":"2007","type":"journal_article","citation":{"mla":"Grüne, L., and O. Junge. “Global Optimal Control of Perturbed Systems.” Journal of Optimization Theory and Applications, 2007, pp. 411–29, doi:10.1007/s10957-007-9312-z.","bibtex":"@article{Grüne_Junge_2007, title={Global Optimal Control of Perturbed Systems}, DOI={10.1007/s10957-007-9312-z}, journal={Journal of Optimization Theory and Applications}, author={Grüne, L. and Junge, O.}, year={2007}, pages={411–429} }","chicago":"Grüne, L., and O. Junge. “Global Optimal Control of Perturbed Systems.” Journal of Optimization Theory and Applications, 2007, 411–29. https://doi.org/10.1007/s10957-007-9312-z.","apa":"Grüne, L., & Junge, O. (2007). Global Optimal Control of Perturbed Systems. Journal of Optimization Theory and Applications, 411–429. https://doi.org/10.1007/s10957-007-9312-z","ama":"Grüne L, Junge O. Global Optimal Control of Perturbed Systems. Journal of Optimization Theory and Applications. 2007:411-429. doi:10.1007/s10957-007-9312-z","ieee":"L. Grüne and O. Junge, “Global Optimal Control of Perturbed Systems,” Journal of Optimization Theory and Applications, pp. 411–429, 2007.","short":"L. Grüne, O. Junge, Journal of Optimization Theory and Applications (2007) 411–429."},"page":"411-429","date_updated":"2022-01-06T06:52:53Z","_id":"16612","doi":"10.1007/s10957-007-9312-z","author":[{"full_name":"Grüne, L.","first_name":"L.","last_name":"Grüne"},{"first_name":"O.","full_name":"Junge, O.","last_name":"Junge"}],"publication":"Journal of Optimization Theory and Applications","department":[{"_id":"101"}],"status":"public","date_created":"2020-04-16T08:03:02Z","publication_status":"published","publication_identifier":{"issn":["0022-3239","1573-2878"]},"user_id":"15701","title":"Global Optimal Control of Perturbed Systems"},{"page":"108-113","citation":{"short":"I. Chaudhuri, S. Sertl, Z. Hajnal, M. Dellnitz, T. Frauenheim, Applied Surface Science (2004) 108–113.","ieee":"I. Chaudhuri, S. Sertl, Z. Hajnal, M. Dellnitz, and T. Frauenheim, “Global optimization of silicon nanoclusters,” Applied Surface Science, pp. 108–113, 2004.","ama":"Chaudhuri I, Sertl S, Hajnal Z, Dellnitz M, Frauenheim T. Global optimization of silicon nanoclusters. Applied Surface Science. 2004:108-113. doi:10.1016/j.apsusc.2003.11.007","apa":"Chaudhuri, I., Sertl, S., Hajnal, Z., Dellnitz, M., & Frauenheim, T. (2004). Global optimization of silicon nanoclusters. Applied Surface Science, 108–113. https://doi.org/10.1016/j.apsusc.2003.11.007","chicago":"Chaudhuri, I., S. Sertl, Z. Hajnal, M. Dellnitz, and Th. Frauenheim. “Global Optimization of Silicon Nanoclusters.” Applied Surface Science, 2004, 108–13. https://doi.org/10.1016/j.apsusc.2003.11.007.","mla":"Chaudhuri, I., et al. “Global Optimization of Silicon Nanoclusters.” Applied Surface Science, 2004, pp. 108–13, doi:10.1016/j.apsusc.2003.11.007.","bibtex":"@article{Chaudhuri_Sertl_Hajnal_Dellnitz_Frauenheim_2004, title={Global optimization of silicon nanoclusters}, DOI={10.1016/j.apsusc.2003.11.007}, journal={Applied Surface Science}, author={Chaudhuri, I. and Sertl, S. and Hajnal, Z. and Dellnitz, M. and Frauenheim, Th.}, year={2004}, pages={108–113} }"},"type":"journal_article","year":"2004","language":[{"iso":"eng"}],"_id":"16500","date_updated":"2022-01-06T06:52:52Z","doi":"10.1016/j.apsusc.2003.11.007","department":[{"_id":"101"}],"publication":"Applied Surface Science","author":[{"last_name":"Chaudhuri","full_name":"Chaudhuri, I.","first_name":"I."},{"last_name":"Sertl","full_name":"Sertl, S.","first_name":"S."},{"full_name":"Hajnal, Z.","first_name":"Z.","last_name":"Hajnal"},{"last_name":"Dellnitz","first_name":"M.","full_name":"Dellnitz, M."},{"first_name":"Th.","full_name":"Frauenheim, Th.","last_name":"Frauenheim"}],"publication_status":"published","publication_identifier":{"issn":["0169-4332"]},"date_created":"2020-04-14T10:08:09Z","status":"public","title":"Global optimization of silicon nanoclusters","user_id":"15701"},{"doi":"10.1007/s10898-005-4384-5","date_updated":"2022-01-06T06:52:54Z","_id":"16671","page":"569-587","year":"2006","citation":{"short":"S. Sertl, M. Dellnitz, Journal of Global Optimization (2006) 569–587.","ieee":"S. Sertl and M. Dellnitz, “Global Optimization using a Dynamical Systems Approach,” Journal of Global Optimization, pp. 569–587, 2006.","chicago":"Sertl, Stefan, and Michael Dellnitz. “Global Optimization Using a Dynamical Systems Approach.” Journal of Global Optimization, 2006, 569–87. https://doi.org/10.1007/s10898-005-4384-5.","apa":"Sertl, S., & Dellnitz, M. (2006). Global Optimization using a Dynamical Systems Approach. Journal of Global Optimization, 569–587. https://doi.org/10.1007/s10898-005-4384-5","ama":"Sertl S, Dellnitz M. Global Optimization using a Dynamical Systems Approach. Journal of Global Optimization. 2006:569-587. doi:10.1007/s10898-005-4384-5","mla":"Sertl, Stefan, and Michael Dellnitz. “Global Optimization Using a Dynamical Systems Approach.” Journal of Global Optimization, 2006, pp. 569–87, doi:10.1007/s10898-005-4384-5.","bibtex":"@article{Sertl_Dellnitz_2006, title={Global Optimization using a Dynamical Systems Approach}, DOI={10.1007/s10898-005-4384-5}, journal={Journal of Global Optimization}, author={Sertl, Stefan and Dellnitz, Michael}, year={2006}, pages={569–587} }"},"type":"journal_article","language":[{"iso":"eng"}],"title":"Global Optimization using a Dynamical Systems Approach","user_id":"15701","publication_identifier":{"issn":["0925-5001","1573-2916"]},"publication_status":"published","date_created":"2020-04-16T10:07:46Z","status":"public","department":[{"_id":"101"}],"publication":"Journal of Global Optimization","author":[{"last_name":"Sertl","first_name":"Stefan","full_name":"Sertl, Stefan"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"}]},{"doi":"10.1007/978-3-319-64063-1_7","date_updated":"2022-01-06T07:04:00Z","_id":"8752","citation":{"mla":"Peitz, Sebastian, and Michael Dellnitz. “Gradient-Based Multiobjective Optimization with Uncertainties.” NEO 2016, 2017, pp. 159–82, doi:10.1007/978-3-319-64063-1_7.","bibtex":"@inproceedings{Peitz_Dellnitz_2017, place={Cham}, title={Gradient-Based Multiobjective Optimization with Uncertainties}, DOI={10.1007/978-3-319-64063-1_7}, booktitle={NEO 2016}, author={Peitz, Sebastian and Dellnitz, Michael}, year={2017}, pages={159–182} }","chicago":"Peitz, Sebastian, and Michael Dellnitz. “Gradient-Based Multiobjective Optimization with Uncertainties.” In NEO 2016, 159–82. Cham, 2017. https://doi.org/10.1007/978-3-319-64063-1_7.","ama":"Peitz S, Dellnitz M. Gradient-Based Multiobjective Optimization with Uncertainties. In: NEO 2016. Cham; 2017:159-182. doi:10.1007/978-3-319-64063-1_7","apa":"Peitz, S., & Dellnitz, M. (2017). Gradient-Based Multiobjective Optimization with Uncertainties. In NEO 2016 (pp. 159–182). Cham. https://doi.org/10.1007/978-3-319-64063-1_7","ieee":"S. Peitz and M. Dellnitz, “Gradient-Based Multiobjective Optimization with Uncertainties,” in NEO 2016, 2017, pp. 159–182.","short":"S. Peitz, M. Dellnitz, in: NEO 2016, Cham, 2017, pp. 159–182."},"type":"conference","year":"2017","page":"159-182","language":[{"iso":"eng"}],"title":"Gradient-Based Multiobjective Optimization with Uncertainties","user_id":"47427","place":"Cham","abstract":[{"lang":"eng","text":"In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties. To this end, an additional condition is derived for the descent direction in order to account for inaccuracies in the gradients and then incorporated into a subdivision algorithm for the computation of global solutions to multiobjective optimization problems. Convergence to a superset of the Pareto set is proved and an upper bound for the maximal distance to the set of substationary points is given. Besides the applicability to problems with uncertainties, the algorithm is developed with the intention to use it in combination with model order reduction techniques in order to efficiently solve PDE-constrained multiobjective optimization problems."}],"publication_identifier":{"issn":["1860-949X","1860-9503"],"isbn":["9783319640624","9783319640631"]},"publication_status":"published","status":"public","date_created":"2019-03-29T13:28:56Z","project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"author":[{"last_name":"Peitz","id":"47427","first_name":"Sebastian","full_name":"Peitz, Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"}],"department":[{"_id":"101"}],"publication":"NEO 2016"},{"year":"2006","citation":{"mla":"Dellnitz, Michael, et al. “Graph Algorithms for Dynamical Systems.” Analysis, Modeling and Simulation of Multiscale Problems, 2006, doi:10.1007/3-540-35657-6_23.","bibtex":"@inbook{Dellnitz_Molo_Metzner_Preis_Schütte_2006, title={Graph Algorithms for Dynamical Systems}, DOI={10.1007/3-540-35657-6_23}, booktitle={Analysis, Modeling and Simulation of Multiscale Problems}, author={Dellnitz, Michael and Molo, Mirko Hessel-von and Metzner, Philipp and Preis, Robert and Schütte, Christof}, year={2006} }","ama":"Dellnitz M, Molo MH, Metzner P, Preis R, Schütte C. Graph Algorithms for Dynamical Systems. In: Analysis, Modeling and Simulation of Multiscale Problems. ; 2006. doi:10.1007/3-540-35657-6_23","apa":"Dellnitz, M., Molo, M. H., Metzner, P., Preis, R., & Schütte, C. (2006). Graph Algorithms for Dynamical Systems. In Analysis, Modeling and Simulation of Multiscale Problems. https://doi.org/10.1007/3-540-35657-6_23","chicago":"Dellnitz, Michael, Mirko Hessel-von Molo, Philipp Metzner, Robert Preis, and Christof Schütte. “Graph Algorithms for Dynamical Systems.” In Analysis, Modeling and Simulation of Multiscale Problems, 2006. https://doi.org/10.1007/3-540-35657-6_23.","ieee":"M. Dellnitz, M. H. Molo, P. Metzner, R. Preis, and C. Schütte, “Graph Algorithms for Dynamical Systems,” in Analysis, Modeling and Simulation of Multiscale Problems, 2006.","short":"M. Dellnitz, M.H. Molo, P. Metzner, R. Preis, C. Schütte, in: Analysis, Modeling and Simulation of Multiscale Problems, 2006."},"type":"book_chapter","doi":"10.1007/3-540-35657-6_23","_id":"16559","date_updated":"2022-01-06T06:52:52Z","status":"public","date_created":"2020-04-15T09:56:14Z","publication_identifier":{"isbn":["9783540356561"]},"publication_status":"published","author":[{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"full_name":"Molo, Mirko Hessel-von","first_name":"Mirko Hessel-von","last_name":"Molo"},{"last_name":"Metzner","first_name":"Philipp","full_name":"Metzner, Philipp"},{"first_name":"Robert","full_name":"Preis, Robert","last_name":"Preis"},{"full_name":"Schütte, Christof","first_name":"Christof","last_name":"Schütte"}],"publication":"Analysis, Modeling and Simulation of Multiscale Problems","department":[{"_id":"101"}],"user_id":"15701","title":"Graph Algorithms for Dynamical Systems"},{"date_updated":"2022-01-06T06:52:54Z","_id":"16659","doi":"10.1080/0305215x.2011.634407","citation":{"ieee":"M. Ringkamp, S. Ober-Blöbaum, M. Dellnitz, and O. Schütze, “Handling high-dimensional problems with multi-objective continuation methods via successive approximation of the tangent space,” Engineering Optimization, pp. 1117–1146, 2012.","short":"M. Ringkamp, S. Ober-Blöbaum, M. Dellnitz, O. Schütze, Engineering Optimization (2012) 1117–1146.","bibtex":"@article{Ringkamp_Ober-Blöbaum_Dellnitz_Schütze_2012, title={Handling high-dimensional problems with multi-objective continuation methods via successive approximation of the tangent space}, DOI={10.1080/0305215x.2011.634407}, journal={Engineering Optimization}, author={Ringkamp, Maik and Ober-Blöbaum, Sina and Dellnitz, Michael and Schütze, Oliver}, year={2012}, pages={1117–1146} }","mla":"Ringkamp, Maik, et al. “Handling High-Dimensional Problems with Multi-Objective Continuation Methods via Successive Approximation of the Tangent Space.” Engineering Optimization, 2012, pp. 1117–46, doi:10.1080/0305215x.2011.634407.","apa":"Ringkamp, M., Ober-Blöbaum, S., Dellnitz, M., & Schütze, O. (2012). Handling high-dimensional problems with multi-objective continuation methods via successive approximation of the tangent space. Engineering Optimization, 1117–1146. https://doi.org/10.1080/0305215x.2011.634407","ama":"Ringkamp M, Ober-Blöbaum S, Dellnitz M, Schütze O. Handling high-dimensional problems with multi-objective continuation methods via successive approximation of the tangent space. Engineering Optimization. 2012:1117-1146. doi:10.1080/0305215x.2011.634407","chicago":"Ringkamp, Maik, Sina Ober-Blöbaum, Michael Dellnitz, and Oliver Schütze. “Handling High-Dimensional Problems with Multi-Objective Continuation Methods via Successive Approximation of the Tangent Space.” Engineering Optimization, 2012, 1117–46. https://doi.org/10.1080/0305215x.2011.634407."},"year":"2012","type":"journal_article","page":"1117-1146","language":[{"iso":"eng"}],"title":"Handling high-dimensional problems with multi-objective continuation methods via successive approximation of the tangent space","user_id":"15701","author":[{"full_name":"Ringkamp, Maik","first_name":"Maik","last_name":"Ringkamp"},{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"},{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"},{"full_name":"Schütze, Oliver","first_name":"Oliver","last_name":"Schütze"}],"publication":"Engineering Optimization","department":[{"_id":"101"}],"publication_status":"published","publication_identifier":{"issn":["0305-215X","1029-0273"]},"status":"public","date_created":"2020-04-16T09:34:05Z"},{"issue":"2","intvolume":" 12","_id":"52726","citation":{"ieee":"C. Bick and S. von der Gracht, “Heteroclinic dynamics in network dynamical systems with higher-order interactions,” Journal of Complex Networks, vol. 12, no. 2, 2024, doi: 10.1093/comnet/cnae009.","short":"C. Bick, S. von der Gracht, Journal of Complex Networks 12 (2024).","bibtex":"@article{Bick_von der Gracht_2024, title={Heteroclinic dynamics in network dynamical systems with higher-order interactions}, volume={12}, DOI={10.1093/comnet/cnae009}, number={2}, journal={Journal of Complex Networks}, publisher={Oxford University Press (OUP)}, author={Bick, Christian and von der Gracht, Sören}, year={2024} }","mla":"Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network Dynamical Systems with Higher-Order Interactions.” Journal of Complex Networks, vol. 12, no. 2, Oxford University Press (OUP), 2024, doi:10.1093/comnet/cnae009.","chicago":"Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network Dynamical Systems with Higher-Order Interactions.” Journal of Complex Networks 12, no. 2 (2024). https://doi.org/10.1093/comnet/cnae009.","apa":"Bick, C., & von der Gracht, S. (2024). Heteroclinic dynamics in network dynamical systems with higher-order interactions. Journal of Complex Networks, 12(2). https://doi.org/10.1093/comnet/cnae009","ama":"Bick C, von der Gracht S. Heteroclinic dynamics in network dynamical systems with higher-order interactions. Journal of Complex Networks. 2024;12(2). doi:10.1093/comnet/cnae009"},"type":"journal_article","year":"2024","main_file_link":[{"url":"https://academic.oup.com/comnet/article-pdf/12/2/cnae009/56832119/cnae009.pdf","open_access":"1"}],"user_id":"97359","ddc":["510"],"article_type":"original","abstract":[{"lang":"eng","text":"Heteroclinic structures organize global features of dynamical systems. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analysed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures."}],"has_accepted_license":"1","status":"public","date_created":"2024-03-22T09:04:57Z","volume":12,"file":[{"access_level":"closed","date_created":"2024-03-22T09:06:07Z","file_name":"heteroclinic-dynamics-in-network-dynamical-systems-with-higher-order-interactions.pdf","relation":"main_file","success":1,"date_updated":"2024-03-22T09:06:07Z","content_type":"application/pdf","file_id":"52728","creator":"svdg","file_size":649155}],"author":[{"last_name":"Bick","full_name":"Bick, Christian","first_name":"Christian"},{"first_name":"Sören","full_name":"von der Gracht, Sören","orcid":"0000-0002-8054-2058","last_name":"von der Gracht","id":"97359"}],"publisher":"Oxford University Press (OUP)","publication":"Journal of Complex Networks","file_date_updated":"2024-03-22T09:06:07Z","keyword":["Applied Mathematics","Computational Mathematics","Control and Optimization","Management Science and Operations Research","Computer Networks and Communications"],"oa":"1","doi":"10.1093/comnet/cnae009","date_updated":"2024-03-22T09:11:53Z","language":[{"iso":"eng"}],"title":"Heteroclinic dynamics in network dynamical systems with higher-order interactions","external_id":{"arxiv":["2309.02006"]},"publication_identifier":{"issn":["2051-1329"]},"publication_status":"published","department":[{"_id":"101"}]},{"author":[{"last_name":"Campos","full_name":"Campos, Cédric M.","first_name":"Cédric M."},{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"full_name":"Trélat, Emmanuel","first_name":"Emmanuel","last_name":"Trélat"}],"publication":"Discrete & Continuous Dynamical Systems - A","department":[{"_id":"101"}],"status":"public","date_created":"2020-05-20T08:21:03Z","volume":35,"user_id":"47427","title":"High order variational integrators in the optimal control of mechanical systems","language":[{"iso":"eng"}],"year":"2015","citation":{"short":"C.M. Campos, S. Ober-Blöbaum, E. Trélat, Discrete & Continuous Dynamical Systems - A 35 (2015) 4193–4223.","ieee":"C. M. Campos, S. Ober-Blöbaum, and E. Trélat, “High order variational integrators in the optimal control of mechanical systems,” Discrete & Continuous Dynamical Systems - A, vol. 35, no. 9, pp. 4193–4223, 2015.","chicago":"Campos, Cédric M., Sina Ober-Blöbaum, and Emmanuel Trélat. “High Order Variational Integrators in the Optimal Control of Mechanical Systems.” Discrete & Continuous Dynamical Systems - A 35, no. 9 (2015): 4193–4223. https://doi.org/10.3934/dcds.2015.35.4193.","ama":"Campos CM, Ober-Blöbaum S, Trélat E. High order variational integrators in the optimal control of mechanical systems. Discrete & Continuous Dynamical Systems - A. 2015;35(9):4193-4223. doi:10.3934/dcds.2015.35.4193","apa":"Campos, C. M., Ober-Blöbaum, S., & Trélat, E. (2015). High order variational integrators in the optimal control of mechanical systems. Discrete & Continuous Dynamical Systems - A, 35(9), 4193–4223. https://doi.org/10.3934/dcds.2015.35.4193","bibtex":"@article{Campos_Ober-Blöbaum_Trélat_2015, title={High order variational integrators in the optimal control of mechanical systems}, volume={35}, DOI={10.3934/dcds.2015.35.4193}, number={9}, journal={Discrete & Continuous Dynamical Systems - A}, author={Campos, Cédric M. and Ober-Blöbaum, Sina and Trélat, Emmanuel}, year={2015}, pages={4193–4223} }","mla":"Campos, Cédric M., et al. “High Order Variational Integrators in the Optimal Control of Mechanical Systems.” Discrete & Continuous Dynamical Systems - A, vol. 35, no. 9, 2015, pp. 4193–223, doi:10.3934/dcds.2015.35.4193."},"type":"journal_article","page":"4193-4223","_id":"17041","date_updated":"2022-01-06T06:53:03Z","intvolume":" 35","issue":"9","doi":"10.3934/dcds.2015.35.4193"},{"language":[{"iso":"eng"}],"year":"2023","type":"preprint","citation":{"ieee":"S. von der Gracht, E. Nijholt, and B. Rink, “Higher order interactions lead to ‘reluctant’ synchrony breaking,” arXiv:2311.17186. 2023.","short":"S. von der Gracht, E. Nijholt, B. Rink, ArXiv:2311.17186 (2023).","bibtex":"@article{von der Gracht_Nijholt_Rink_2023, title={Higher order interactions lead to “reluctant” synchrony breaking}, journal={arXiv:2311.17186}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2023} }","mla":"von der Gracht, Sören, et al. “Higher Order Interactions Lead to ‘Reluctant’ Synchrony Breaking.” ArXiv:2311.17186, 2023.","apa":"von der Gracht, S., Nijholt, E., & Rink, B. (2023). Higher order interactions lead to “reluctant” synchrony breaking. In arXiv:2311.17186.","ama":"von der Gracht S, Nijholt E, Rink B. Higher order interactions lead to “reluctant” synchrony breaking. arXiv:231117186. Published online 2023.","chicago":"Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Higher Order Interactions Lead to ‘Reluctant’ Synchrony Breaking.” ArXiv:2311.17186, 2023."},"_id":"49371","date_updated":"2023-12-01T06:38:44Z","author":[{"id":"97359","last_name":"von der Gracht","orcid":"0000-0002-8054-2058","full_name":"von der Gracht, Sören","first_name":"Sören"},{"last_name":"Nijholt","first_name":"Eddie","full_name":"Nijholt, Eddie"},{"first_name":"Bob","full_name":"Rink, Bob","last_name":"Rink"}],"publication":"arXiv:2311.17186","department":[{"_id":"101"}],"status":"public","date_created":"2023-12-01T06:35:29Z","abstract":[{"text":"To model dynamical systems on networks with higher order (non-pairwise)\r\ninteractions, we recently introduced a new class of ODEs on hypernetworks. Here\r\nwe consider one-parameter synchrony breaking bifurcations in such ODEs. We call\r\na synchrony breaking steady state branch \"reluctant\" if it is tangent to a\r\nsynchrony space, but does not lie inside it. We prove that reluctant synchrony\r\nbreaking is ubiquitous in hypernetwork systems, by constructing a large class\r\nof examples that support it. We also give an explicit formula for the order of\r\ntangency to the synchrony space of a reluctant steady state branch.","lang":"eng"}],"external_id":{"arxiv":["2311.17186"]},"user_id":"97359","title":"Higher order interactions lead to \"reluctant\" synchrony breaking"},{"_id":"16667","date_updated":"2022-01-06T06:52:54Z","doi":"10.1080/03052150701821328","citation":{"mla":"Schütze, Oliver, et al. “Hybridizing Evolutionary Strategies with Continuation Methods for Solving Multi-Objective Problems.” Engineering Optimization, 2008, pp. 383–402, doi:10.1080/03052150701821328.","bibtex":"@article{Schütze_Coello Coello_Mostaghim_Talbi_Dellnitz_2008, title={Hybridizing evolutionary strategies with continuation methods for solving multi-objective problems}, DOI={10.1080/03052150701821328}, journal={Engineering Optimization}, author={Schütze, Oliver and Coello Coello, Carlos A. and Mostaghim, Sanaz and Talbi, El-Ghazali and Dellnitz, Michael}, year={2008}, pages={383–402} }","chicago":"Schütze, Oliver, Carlos A. Coello Coello, Sanaz Mostaghim, El-Ghazali Talbi, and Michael Dellnitz. “Hybridizing Evolutionary Strategies with Continuation Methods for Solving Multi-Objective Problems.” Engineering Optimization, 2008, 383–402. https://doi.org/10.1080/03052150701821328.","apa":"Schütze, O., Coello Coello, C. A., Mostaghim, S., Talbi, E.-G., & Dellnitz, M. (2008). Hybridizing evolutionary strategies with continuation methods for solving multi-objective problems. Engineering Optimization, 383–402. https://doi.org/10.1080/03052150701821328","ama":"Schütze O, Coello Coello CA, Mostaghim S, Talbi E-G, Dellnitz M. Hybridizing evolutionary strategies with continuation methods for solving multi-objective problems. Engineering Optimization. 2008:383-402. doi:10.1080/03052150701821328","ieee":"O. Schütze, C. A. Coello Coello, S. Mostaghim, E.-G. Talbi, and M. Dellnitz, “Hybridizing evolutionary strategies with continuation methods for solving multi-objective problems,” Engineering Optimization, pp. 383–402, 2008.","short":"O. Schütze, C.A. Coello Coello, S. Mostaghim, E.-G. Talbi, M. Dellnitz, Engineering Optimization (2008) 383–402."},"type":"journal_article","year":"2008","page":"383-402","language":[{"iso":"eng"}],"title":"Hybridizing evolutionary strategies with continuation methods for solving multi-objective problems","user_id":"15701","author":[{"full_name":"Schütze, Oliver","first_name":"Oliver","last_name":"Schütze"},{"last_name":"Coello Coello","full_name":"Coello Coello, Carlos A.","first_name":"Carlos A."},{"full_name":"Mostaghim, Sanaz","first_name":"Sanaz","last_name":"Mostaghim"},{"last_name":"Talbi","full_name":"Talbi, El-Ghazali","first_name":"El-Ghazali"},{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"}],"department":[{"_id":"101"}],"publication":"Engineering Optimization","publication_identifier":{"issn":["0305-215X","1029-0273"]},"publication_status":"published","status":"public","date_created":"2020-04-16T10:01:07Z"},{"page":"2329-2353","citation":{"ama":"von der Gracht S, Nijholt E, Rink B. Hypernetworks: Cluster Synchronization Is a Higher-Order Effect. SIAM Journal on Applied Mathematics. 2023;83(6):2329-2353. doi:10.1137/23m1561075","apa":"von der Gracht, S., Nijholt, E., & Rink, B. (2023). Hypernetworks: Cluster Synchronization Is a Higher-Order Effect. SIAM Journal on Applied Mathematics, 83(6), 2329–2353. https://doi.org/10.1137/23m1561075","chicago":"Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Hypernetworks: Cluster Synchronization Is a Higher-Order Effect.” SIAM Journal on Applied Mathematics 83, no. 6 (2023): 2329–53. https://doi.org/10.1137/23m1561075.","mla":"von der Gracht, Sören, et al. “Hypernetworks: Cluster Synchronization Is a Higher-Order Effect.” SIAM Journal on Applied Mathematics, vol. 83, no. 6, Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 2329–53, doi:10.1137/23m1561075.","bibtex":"@article{von der Gracht_Nijholt_Rink_2023, title={Hypernetworks: Cluster Synchronization Is a Higher-Order Effect}, volume={83}, DOI={10.1137/23m1561075}, number={6}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2023}, pages={2329–2353} }","short":"S. von der Gracht, E. Nijholt, B. Rink, SIAM Journal on Applied Mathematics 83 (2023) 2329–2353.","ieee":"S. von der Gracht, E. Nijholt, and B. Rink, “Hypernetworks: Cluster Synchronization Is a Higher-Order Effect,” SIAM Journal on Applied Mathematics, vol. 83, no. 6, pp. 2329–2353, 2023, doi: 10.1137/23m1561075."},"type":"journal_article","year":"2023","issue":"6","_id":"49326","intvolume":" 83","volume":83,"date_created":"2023-11-29T10:50:05Z","status":"public","publication":"SIAM Journal on Applied Mathematics","keyword":["Applied Mathematics"],"publisher":"Society for Industrial & Applied Mathematics (SIAM)","author":[{"full_name":"von der Gracht, Sören","orcid":"0000-0002-8054-2058","first_name":"Sören","id":"97359","last_name":"von der Gracht"},{"full_name":"Nijholt, Eddie","first_name":"Eddie","last_name":"Nijholt"},{"first_name":"Bob","full_name":"Rink, Bob","last_name":"Rink"}],"user_id":"97359","abstract":[{"text":"Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by defining a class of admissible maps for every such hypernetwork. We explain how to classify robust cluster synchronization patterns on hypernetworks by finding balanced partitions, and we generalize the concept of a graph fibration to the hypernetwork context. We also show that robust synchronization patterns are only fully determined by polynomial admissible maps of high order. This means that, unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order, i.e., nonlinear, effect. We give a formula, in terms of the order of the hypernetwork, for the degree of the polynomial admissible maps that determine robust synchronization patterns. We also demonstrate that this degree is optimal by investigating a class of examples. We conclude by demonstrating how this effect may cause remarkable synchrony breaking bifurcations that occur at high polynomial degree.","lang":"eng"}],"language":[{"iso":"eng"}],"doi":"10.1137/23m1561075","date_updated":"2023-11-29T10:52:23Z","publication_status":"published","publication_identifier":{"issn":["0036-1399","1095-712X"]},"department":[{"_id":"101"}],"title":"Hypernetworks: Cluster Synchronization Is a Higher-Order Effect","external_id":{"arxiv":["2302.08974"]}},{"language":[{"iso":"eng"}],"citation":{"short":"C. Gölz, C. Voelcker-Rehage, K. Mora, E.-M. Reuter, B. Godde, M. Dellnitz, C. Reinsberger, S. Vieluf, Frontiers in Physiology (2018).","ieee":"C. Gölz et al., “Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics,” Frontiers in Physiology, 2018.","ama":"Gölz C, Voelcker-Rehage C, Mora K, et al. Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics. Frontiers in Physiology. 2018. doi:10.3389/fphys.2018.01540","apa":"Gölz, C., Voelcker-Rehage, C., Mora, K., Reuter, E.-M., Godde, B., Dellnitz, M., … Vieluf, S. (2018). Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics. Frontiers in Physiology. https://doi.org/10.3389/fphys.2018.01540","chicago":"Gölz, Christian, Claudia Voelcker-Rehage, Karin Mora, Eva-Maria Reuter, Ben Godde, Michael Dellnitz, Claus Reinsberger, and Solveig Vieluf. “Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics.” Frontiers in Physiology, 2018. https://doi.org/10.3389/fphys.2018.01540.","mla":"Gölz, Christian, et al. “Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics.” Frontiers in Physiology, 2018, doi:10.3389/fphys.2018.01540.","bibtex":"@article{Gölz_Voelcker-Rehage_Mora_Reuter_Godde_Dellnitz_Reinsberger_Vieluf_2018, title={Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics}, DOI={10.3389/fphys.2018.01540}, journal={Frontiers in Physiology}, author={Gölz, Christian and Voelcker-Rehage, Claudia and Mora, Karin and Reuter, Eva-Maria and Godde, Ben and Dellnitz, Michael and Reinsberger, Claus and Vieluf, Solveig}, year={2018} }"},"year":"2018","type":"journal_article","doi":"10.3389/fphys.2018.01540","_id":"16713","date_updated":"2022-01-06T06:52:55Z","status":"public","date_created":"2020-04-16T14:08:06Z","publication_status":"published","publication_identifier":{"issn":["1664-042X"]},"author":[{"last_name":"Gölz","full_name":"Gölz, Christian","first_name":"Christian"},{"last_name":"Voelcker-Rehage","full_name":"Voelcker-Rehage, Claudia","first_name":"Claudia"},{"last_name":"Mora","first_name":"Karin","full_name":"Mora, Karin"},{"last_name":"Reuter","full_name":"Reuter, Eva-Maria","first_name":"Eva-Maria"},{"last_name":"Godde","full_name":"Godde, Ben","first_name":"Ben"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"},{"last_name":"Reinsberger","full_name":"Reinsberger, Claus","first_name":"Claus"},{"first_name":"Solveig","full_name":"Vieluf, Solveig","last_name":"Vieluf"}],"publication":"Frontiers in Physiology","department":[{"_id":"101"}],"user_id":"47427","title":"Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics"},{"language":[{"iso":"eng"}],"type":"journal_article","year":"2012","citation":{"mla":"Zanzottera, A., et al. “Intersecting Invariant Manifolds in Spatial Restricted Three-Body Problems: Design and Optimization of Earth-to-Halo Transfers in the Sun–Earth–Moon Scenario.” Communications in Nonlinear Science and Numerical Simulation, 2012, pp. 832–43, doi:10.1016/j.cnsns.2011.06.032.","bibtex":"@article{Zanzottera_Mingotti_Castelli_Dellnitz_2012, title={Intersecting invariant manifolds in spatial restricted three-body problems: Design and optimization of Earth-to-halo transfers in the Sun–Earth–Moon scenario}, DOI={10.1016/j.cnsns.2011.06.032}, journal={Communications in Nonlinear Science and Numerical Simulation}, author={Zanzottera, A. and Mingotti, G. and Castelli, R. and Dellnitz, M.}, year={2012}, pages={832–843} }","chicago":"Zanzottera, A., G. Mingotti, R. Castelli, and M. Dellnitz. “Intersecting Invariant Manifolds in Spatial Restricted Three-Body Problems: Design and Optimization of Earth-to-Halo Transfers in the Sun–Earth–Moon Scenario.” Communications in Nonlinear Science and Numerical Simulation, 2012, 832–43. https://doi.org/10.1016/j.cnsns.2011.06.032.","ama":"Zanzottera A, Mingotti G, Castelli R, Dellnitz M. Intersecting invariant manifolds in spatial restricted three-body problems: Design and optimization of Earth-to-halo transfers in the Sun–Earth–Moon scenario. Communications in Nonlinear Science and Numerical Simulation. 2012:832-843. doi:10.1016/j.cnsns.2011.06.032","apa":"Zanzottera, A., Mingotti, G., Castelli, R., & Dellnitz, M. (2012). Intersecting invariant manifolds in spatial restricted three-body problems: Design and optimization of Earth-to-halo transfers in the Sun–Earth–Moon scenario. Communications in Nonlinear Science and Numerical Simulation, 832–843. https://doi.org/10.1016/j.cnsns.2011.06.032","ieee":"A. Zanzottera, G. Mingotti, R. Castelli, and M. Dellnitz, “Intersecting invariant manifolds in spatial restricted three-body problems: Design and optimization of Earth-to-halo transfers in the Sun–Earth–Moon scenario,” Communications in Nonlinear Science and Numerical Simulation, pp. 832–843, 2012.","short":"A. Zanzottera, G. Mingotti, R. Castelli, M. Dellnitz, Communications in Nonlinear Science and Numerical Simulation (2012) 832–843."},"page":"832-843","date_updated":"2022-01-06T06:52:54Z","_id":"16696","doi":"10.1016/j.cnsns.2011.06.032","author":[{"last_name":"Zanzottera","full_name":"Zanzottera, A.","first_name":"A."},{"last_name":"Mingotti","first_name":"G.","full_name":"Mingotti, G."},{"first_name":"R.","full_name":"Castelli, R.","last_name":"Castelli"},{"last_name":"Dellnitz","full_name":"Dellnitz, M.","first_name":"M."}],"department":[{"_id":"101"}],"publication":"Communications in Nonlinear Science and Numerical Simulation","status":"public","date_created":"2020-04-16T10:56:56Z","publication_status":"published","publication_identifier":{"issn":["1007-5704"]},"user_id":"15701","title":"Intersecting invariant manifolds in spatial restricted three-body problems: Design and optimization of Earth-to-halo transfers in the Sun–Earth–Moon scenario"},{"abstract":[{"lang":"eng","text":"It is a challenging task to identify the objectives on which a certain decision was based, in particular if several, potentially conflicting criteria are equally important and a continuous set of optimal compromise decisions exists. This task can be understood as the inverse problem of multiobjective optimization, where the goal is to find the objective function vector of a given Pareto set. To this end, we present a method to construct the objective function vector of an unconstrained multiobjective optimization problem (MOP) such that the Pareto critical set contains a given set of data points with prescribed KKT multipliers. If such an MOP can not be found, then the method instead produces an MOP whose Pareto critical set is at least close to the data points. The key idea is to consider the objective function vector in the multiobjective KKT conditions as variable and then search for the objectives that minimize the Euclidean norm of the resulting system of equations. By expressing the objectives in a finite-dimensional basis, we transform this problem into a homogeneous, linear system of equations that can be solved efficiently. Potential applications of this approach include the identification of objectives (both from clean and noisy data) and the construction of surrogate models for expensive MOPs."}],"user_id":"47427","publication":"Journal of Global Optimization","author":[{"last_name":"Gebken","id":"32643","first_name":"Bennet","full_name":"Gebken, Bennet"},{"first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","last_name":"Peitz","id":"47427"}],"publisher":"Springer","date_created":"2020-03-13T12:45:05Z","status":"public","volume":80,"_id":"16295","intvolume":" 80","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10898-020-00983-z.pdf","open_access":"1"}],"page":"3-29","type":"journal_article","year":"2021","citation":{"bibtex":"@article{Gebken_Peitz_2021, title={Inverse multiobjective optimization: Inferring decision criteria from data}, volume={80}, DOI={10.1007/s10898-020-00983-z}, journal={Journal of Global Optimization}, publisher={Springer}, author={Gebken, Bennet and Peitz, Sebastian}, year={2021}, pages={3–29} }","mla":"Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization: Inferring Decision Criteria from Data.” Journal of Global Optimization, vol. 80, Springer, 2021, pp. 3–29, doi:10.1007/s10898-020-00983-z.","apa":"Gebken, B., & Peitz, S. (2021). Inverse multiobjective optimization: Inferring decision criteria from data. Journal of Global Optimization, 80, 3–29. https://doi.org/10.1007/s10898-020-00983-z","ama":"Gebken B, Peitz S. Inverse multiobjective optimization: Inferring decision criteria from data. Journal of Global Optimization. 2021;80:3-29. doi:10.1007/s10898-020-00983-z","chicago":"Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization: Inferring Decision Criteria from Data.” Journal of Global Optimization 80 (2021): 3–29. https://doi.org/10.1007/s10898-020-00983-z.","ieee":"B. Gebken and S. Peitz, “Inverse multiobjective optimization: Inferring decision criteria from data,” Journal of Global Optimization, vol. 80, pp. 3–29, 2021.","short":"B. Gebken, S. Peitz, Journal of Global Optimization 80 (2021) 3–29."},"title":"Inverse multiobjective optimization: Inferring decision criteria from data","department":[{"_id":"101"}],"date_updated":"2022-01-06T06:52:48Z","oa":"1","doi":"10.1007/s10898-020-00983-z","language":[{"iso":"eng"}]},{"main_file_link":[{"open_access":"1","url":"https://www.mdpi.com/1099-4300/22/7/722"}],"language":[{"iso":"eng"}],"year":"2020","type":"journal_article","citation":{"short":"S. Klus, F. Nüske, B. Hamzi, Entropy (2020).","ieee":"S. Klus, F. Nüske, and B. Hamzi, “Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator,” Entropy, 2020.","chicago":"Klus, Stefan, Feliks Nüske, and Boumediene Hamzi. “Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator.” Entropy, 2020. https://doi.org/10.3390/e22070722.","apa":"Klus, S., Nüske, F., & Hamzi, B. (2020). Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator. Entropy. https://doi.org/10.3390/e22070722","ama":"Klus S, Nüske F, Hamzi B. Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator. Entropy. 2020. doi:10.3390/e22070722","mla":"Klus, Stefan, et al. “Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator.” Entropy, 722, 2020, doi:10.3390/e22070722.","bibtex":"@article{Klus_Nüske_Hamzi_2020, title={Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator}, DOI={10.3390/e22070722}, number={722}, journal={Entropy}, author={Klus, Stefan and Nüske, Feliks and Hamzi, Boumediene}, year={2020} }"},"date_updated":"2022-01-06T06:55:16Z","_id":"21819","oa":"1","doi":"10.3390/e22070722","article_number":"722","department":[{"_id":"101"}],"publication":"Entropy","author":[{"last_name":"Klus","first_name":"Stefan","full_name":"Klus, Stefan"},{"first_name":"Feliks","orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks","last_name":"Nüske","id":"81513"},{"first_name":"Boumediene","full_name":"Hamzi, Boumediene","last_name":"Hamzi"}],"date_created":"2021-04-28T18:06:35Z","status":"public","publication_identifier":{"issn":["1099-4300"]},"publication_status":"published","abstract":[{"text":"Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schrödinger operator. We propose a kernel-based method for the approximation of differential operators in reproducing kernel Hilbert spaces and show how eigenfunctions can be estimated by solving auxiliary matrix eigenvalue problems. The resulting algorithms are applied to molecular dynamics and quantum chemistry examples. Furthermore, we exploit that, under certain conditions, the Schrödinger operator can be transformed into a Kolmogorov backward operator corresponding to a drift-diffusion process and vice versa. This allows us to apply methods developed for the analysis of high-dimensional stochastic differential equations to quantum mechanical systems.","lang":"eng"}],"user_id":"81513","title":"Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator"},{"publication_status":"published","department":[{"_id":"655"},{"_id":"101"}],"title":"Koopman analysis of quantum systems","external_id":{"arxiv":["2201.12062"]},"language":[{"iso":"eng"}],"oa":"1","doi":"10.1088/1751-8121/ac7d22","date_updated":"2022-07-18T14:26:41Z","status":"public","date_created":"2022-01-31T09:49:40Z","volume":55,"publisher":"IOP Publishing Ltd.","author":[{"last_name":"Klus","first_name":"Stefan","full_name":"Klus, Stefan"},{"first_name":"Feliks","orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks","last_name":"Nüske","id":"81513"},{"full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian","id":"47427","last_name":"Peitz"}],"publication":"Journal of Physics A: Mathematical and Theoretical","user_id":"47427","abstract":[{"text":"Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular dynamics, climate science, engineering, and biology. Applications include detecting metastable or coherent sets, coarse-graining, system identification, and control. There is an intricate connection between dynamical systems driven by stochastic differential equations and quantum mechanics. In this paper, we compare the ground-state transformation and Nelson's stochastic mechanics and demonstrate how data-driven methods developed for the approximation of the Koopman operator can be used to analyze quantum physics problems. Moreover, we exploit the relationship between Schrödinger operators and stochastic control problems to show that modern data-driven methods for stochastic control can be used to solve the stationary or imaginary-time Schrödinger equation. Our findings open up a new avenue towards solving Schrödinger's equation using recently developed tools from data science.","lang":"eng"}],"type":"journal_article","citation":{"chicago":"Klus, Stefan, Feliks Nüske, and Sebastian Peitz. “Koopman Analysis of Quantum Systems.” Journal of Physics A: Mathematical and Theoretical 55, no. 31 (2022): 314002. https://doi.org/10.1088/1751-8121/ac7d22.","ama":"Klus S, Nüske F, Peitz S. Koopman analysis of quantum systems. Journal of Physics A: Mathematical and Theoretical. 2022;55(31):314002. doi:10.1088/1751-8121/ac7d22","apa":"Klus, S., Nüske, F., & Peitz, S. (2022). Koopman analysis of quantum systems. Journal of Physics A: Mathematical and Theoretical, 55(31), 314002. https://doi.org/10.1088/1751-8121/ac7d22","mla":"Klus, Stefan, et al. “Koopman Analysis of Quantum Systems.” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 31, IOP Publishing Ltd., 2022, p. 314002, doi:10.1088/1751-8121/ac7d22.","bibtex":"@article{Klus_Nüske_Peitz_2022, title={Koopman analysis of quantum systems}, volume={55}, DOI={10.1088/1751-8121/ac7d22}, number={31}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing Ltd.}, author={Klus, Stefan and Nüske, Feliks and Peitz, Sebastian}, year={2022}, pages={314002} }","short":"S. Klus, F. Nüske, S. Peitz, Journal of Physics A: Mathematical and Theoretical 55 (2022) 314002.","ieee":"S. Klus, F. Nüske, and S. Peitz, “Koopman analysis of quantum systems,” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 31, p. 314002, 2022, doi: 10.1088/1751-8121/ac7d22."},"year":"2022","page":"314002","main_file_link":[{"url":"https://iopscience.iop.org/article/10.1088/1751-8121/ac7d22/pdf","open_access":"1"}],"issue":"31","_id":"29673","intvolume":" 55"},{"oa":"1","date_updated":"2022-01-06T06:55:08Z","_id":"21634","language":[{"iso":"eng"}],"citation":{"apa":"Hanke, S., Peitz, S., Wallscheid, O., Klus, S., Böcker, J., & Dellnitz, M. (2018). Koopman Operator-Based Finite-Control-Set Model Predictive Control for Electrical Drives. ArXiv:1804.00854.","ama":"Hanke S, Peitz S, Wallscheid O, Klus S, Böcker J, Dellnitz M. Koopman Operator-Based Finite-Control-Set Model Predictive Control for Electrical Drives. arXiv:180400854. 2018.","chicago":"Hanke, Sören, Sebastian Peitz, Oliver Wallscheid, Stefan Klus, Joachim Böcker, and Michael Dellnitz. “Koopman Operator-Based Finite-Control-Set Model Predictive Control for Electrical Drives.” ArXiv:1804.00854, 2018.","mla":"Hanke, Sören, et al. “Koopman Operator-Based Finite-Control-Set Model Predictive Control for Electrical Drives.” ArXiv:1804.00854, 2018.","bibtex":"@article{Hanke_Peitz_Wallscheid_Klus_Böcker_Dellnitz_2018, title={Koopman Operator-Based Finite-Control-Set Model Predictive Control for Electrical Drives}, journal={arXiv:1804.00854}, author={Hanke, Sören and Peitz, Sebastian and Wallscheid, Oliver and Klus, Stefan and Böcker, Joachim and Dellnitz, Michael}, year={2018} }","short":"S. Hanke, S. Peitz, O. Wallscheid, S. Klus, J. Böcker, M. Dellnitz, ArXiv:1804.00854 (2018).","ieee":"S. Hanke, S. Peitz, O. Wallscheid, S. Klus, J. Böcker, and M. Dellnitz, “Koopman Operator-Based Finite-Control-Set Model Predictive Control for Electrical Drives,” arXiv:1804.00854. 2018."},"type":"preprint","year":"2018","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/1804.00854.pdf"}],"user_id":"47427","title":"Koopman Operator-Based Finite-Control-Set Model Predictive Control for Electrical Drives","abstract":[{"text":"Predictive control of power electronic systems always requires a suitable\r\nmodel of the plant. Using typical physics-based white box models, a trade-off\r\nbetween model complexity (i.e. accuracy) and computational burden has to be\r\nmade. This is a challenging task with a lot of constraints, since the model\r\norder is directly linked to the number of system states. Even though white-box\r\nmodels show suitable performance in most cases, parasitic real-world effects\r\noften cannot be modeled satisfactorily with an expedient computational load.\r\nHence, a Koopman operator-based model reduction technique is presented which\r\ndirectly links the control action to the system's outputs in a black-box\r\nfashion. The Koopman operator is a linear but infinite-dimensional operator\r\ndescribing the dynamics of observables of nonlinear autonomous dynamical\r\nsystems which can be nicely applied to the switching principle of power\r\nelectronic devices. Following this data-driven approach, the model order and\r\nthe number of system states are decoupled which allows us to consider more\r\ncomplex systems. Extensive experimental tests with an automotive-type permanent\r\nmagnet synchronous motor fed by an IGBT 2-level inverter prove the feasibility\r\nof the proposed modeling technique in a finite-set model predictive control\r\napplication.","lang":"eng"}],"date_created":"2021-04-19T16:17:30Z","status":"public","department":[{"_id":"101"}],"publication":"arXiv:1804.00854","author":[{"last_name":"Hanke","full_name":"Hanke, Sören","first_name":"Sören"},{"id":"47427","last_name":"Peitz","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian"},{"full_name":"Wallscheid, Oliver","first_name":"Oliver","last_name":"Wallscheid"},{"last_name":"Klus","full_name":"Klus, Stefan","first_name":"Stefan"},{"full_name":"Böcker, Joachim","first_name":"Joachim","last_name":"Böcker"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}]},{"page":"184-191","citation":{"short":"S. Peitz, S. Klus, Automatica 106 (2019) 184–191.","ieee":"S. Peitz and S. Klus, “Koopman operator-based model reduction for switched-system control of PDEs,” Automatica, vol. 106, pp. 184–191, 2019.","chicago":"Peitz, Sebastian, and Stefan Klus. “Koopman Operator-Based Model Reduction for Switched-System Control of PDEs.” Automatica 106 (2019): 184–91. https://doi.org/10.1016/j.automatica.2019.05.016.","ama":"Peitz S, Klus S. Koopman operator-based model reduction for switched-system control of PDEs. Automatica. 2019;106:184-191. doi:10.1016/j.automatica.2019.05.016","apa":"Peitz, S., & Klus, S. (2019). Koopman operator-based model reduction for switched-system control of PDEs. Automatica, 106, 184–191. https://doi.org/10.1016/j.automatica.2019.05.016","mla":"Peitz, Sebastian, and Stefan Klus. “Koopman Operator-Based Model Reduction for Switched-System Control of PDEs.” Automatica, vol. 106, 2019, pp. 184–91, doi:10.1016/j.automatica.2019.05.016.","bibtex":"@article{Peitz_Klus_2019, title={Koopman operator-based model reduction for switched-system control of PDEs}, volume={106}, DOI={10.1016/j.automatica.2019.05.016}, journal={Automatica}, author={Peitz, Sebastian and Klus, Stefan}, year={2019}, pages={184–191} }"},"year":"2019","type":"journal_article","intvolume":" 106","_id":"10593","date_created":"2019-07-10T08:08:16Z","status":"public","volume":106,"publication":"Automatica","author":[{"orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian","id":"47427","last_name":"Peitz"},{"full_name":"Klus, Stefan","first_name":"Stefan","last_name":"Klus"}],"user_id":"47427","abstract":[{"text":"We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimensional operator which describes the dynamics of observables. A numerical approximation of the Koopman operator therefore yields a linear system for the observation of an autonomous dynamical system. In our approach, by introducing a finite number of constant controls, the dynamic control system is transformed into a set of autonomous systems and the corresponding optimal control problem into a switching time optimization problem. This allows us to replace each of these systems by a K-ROM which can be solved orders of magnitude faster. By this approach, a nonlinear infinite-dimensional control problem is transformed into a low-dimensional linear problem. Using a recent convergence result for the numerical approximation via Extended Dynamic Mode Decomposition (EDMD), we show that the value of the K-ROM based objective function converges in measure to the value of the full objective function. To illustrate the results, we consider the 1D Burgers equation and the 2D Navier–Stokes equations. The numerical experiments show remarkable performance concerning both solution times and accuracy.","lang":"eng"}],"article_type":"original","language":[{"iso":"eng"}],"doi":"10.1016/j.automatica.2019.05.016","date_updated":"2022-01-06T06:50:46Z","publication_identifier":{"issn":["0005-1098"]},"publication_status":"published","department":[{"_id":"101"}],"title":"Koopman operator-based model reduction for switched-system control of PDEs"},{"department":[{"_id":"101"}],"publication":"New Journal of Physics","author":[{"last_name":"Padberg","full_name":"Padberg, Kathrin","first_name":"Kathrin"},{"last_name":"Hauff","first_name":"Thilo","full_name":"Hauff, Thilo"},{"first_name":"Frank","full_name":"Jenko, Frank","last_name":"Jenko"},{"last_name":"Junge","first_name":"Oliver","full_name":"Junge, Oliver"}],"publication_identifier":{"issn":["1367-2630"]},"publication_status":"published","date_created":"2020-04-16T09:10:26Z","status":"public","title":"Lagrangian structures and transport in turbulent magnetized plasmas","user_id":"15701","page":"400-400","citation":{"ieee":"K. Padberg, T. Hauff, F. Jenko, and O. Junge, “Lagrangian structures and transport in turbulent magnetized plasmas,” New Journal of Physics, pp. 400–400, 2007.","short":"K. Padberg, T. Hauff, F. Jenko, O. Junge, New Journal of Physics (2007) 400–400.","bibtex":"@article{Padberg_Hauff_Jenko_Junge_2007, title={Lagrangian structures and transport in turbulent magnetized plasmas}, DOI={10.1088/1367-2630/9/11/400}, journal={New Journal of Physics}, author={Padberg, Kathrin and Hauff, Thilo and Jenko, Frank and Junge, Oliver}, year={2007}, pages={400–400} }","mla":"Padberg, Kathrin, et al. “Lagrangian Structures and Transport in Turbulent Magnetized Plasmas.” New Journal of Physics, 2007, pp. 400–400, doi:10.1088/1367-2630/9/11/400.","ama":"Padberg K, Hauff T, Jenko F, Junge O. Lagrangian structures and transport in turbulent magnetized plasmas. New Journal of Physics. 2007:400-400. doi:10.1088/1367-2630/9/11/400","apa":"Padberg, K., Hauff, T., Jenko, F., & Junge, O. (2007). Lagrangian structures and transport in turbulent magnetized plasmas. New Journal of Physics, 400–400. https://doi.org/10.1088/1367-2630/9/11/400","chicago":"Padberg, Kathrin, Thilo Hauff, Frank Jenko, and Oliver Junge. “Lagrangian Structures and Transport in Turbulent Magnetized Plasmas.” New Journal of Physics, 2007, 400–400. https://doi.org/10.1088/1367-2630/9/11/400."},"year":"2007","type":"journal_article","date_updated":"2022-01-06T06:52:53Z","_id":"16648","doi":"10.1088/1367-2630/9/11/400"},{"page":"4176-4190","type":"journal_article","year":"2009","citation":{"chicago":"Padberg, Kathrin, Bianca Thiere, Robert Preis, and Michael Dellnitz. “Local Expansion Concepts for Detecting Transport Barriers in Dynamical Systems.” Communications in Nonlinear Science and Numerical Simulation, 2009, 4176–90. https://doi.org/10.1016/j.cnsns.2009.03.018.","apa":"Padberg, K., Thiere, B., Preis, R., & Dellnitz, M. (2009). Local expansion concepts for detecting transport barriers in dynamical systems. Communications in Nonlinear Science and Numerical Simulation, 4176–4190. https://doi.org/10.1016/j.cnsns.2009.03.018","ama":"Padberg K, Thiere B, Preis R, Dellnitz M. Local expansion concepts for detecting transport barriers in dynamical systems. Communications in Nonlinear Science and Numerical Simulation. 2009:4176-4190. doi:10.1016/j.cnsns.2009.03.018","bibtex":"@article{Padberg_Thiere_Preis_Dellnitz_2009, title={Local expansion concepts for detecting transport barriers in dynamical systems}, DOI={10.1016/j.cnsns.2009.03.018}, journal={Communications in Nonlinear Science and Numerical Simulation}, author={Padberg, Kathrin and Thiere, Bianca and Preis, Robert and Dellnitz, Michael}, year={2009}, pages={4176–4190} }","mla":"Padberg, Kathrin, et al. “Local Expansion Concepts for Detecting Transport Barriers in Dynamical Systems.” Communications in Nonlinear Science and Numerical Simulation, 2009, pp. 4176–90, doi:10.1016/j.cnsns.2009.03.018.","short":"K. Padberg, B. Thiere, R. Preis, M. Dellnitz, Communications in Nonlinear Science and Numerical Simulation (2009) 4176–4190.","ieee":"K. Padberg, B. Thiere, R. Preis, and M. Dellnitz, “Local expansion concepts for detecting transport barriers in dynamical systems,” Communications in Nonlinear Science and Numerical Simulation, pp. 4176–4190, 2009."},"language":[{"iso":"eng"}],"doi":"10.1016/j.cnsns.2009.03.018","date_updated":"2022-01-06T06:52:53Z","_id":"16649","publication_identifier":{"issn":["1007-5704"]},"publication_status":"published","date_created":"2020-04-16T09:11:26Z","status":"public","publication":"Communications in Nonlinear Science and Numerical Simulation","department":[{"_id":"101"}],"author":[{"last_name":"Padberg","first_name":"Kathrin","full_name":"Padberg, Kathrin"},{"last_name":"Thiere","first_name":"Bianca","full_name":"Thiere, Bianca"},{"last_name":"Preis","full_name":"Preis, Robert","first_name":"Robert"},{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"}],"title":"Local expansion concepts for detecting transport barriers in dynamical systems","user_id":"15701"},{"citation":{"ieee":"G. Froyland, “Markov modelling for random dynamical systems,” in Equadiff 99, 2013.","short":"G. Froyland, in: Equadiff 99, 2013.","bibtex":"@inbook{Froyland_2013, title={Markov modelling for random dynamical systems}, DOI={10.1142/9789812792617_0200}, booktitle={Equadiff 99}, author={Froyland, Gary}, year={2013} }","mla":"Froyland, Gary. “Markov Modelling for Random Dynamical Systems.” Equadiff 99, 2013, doi:10.1142/9789812792617_0200.","apa":"Froyland, G. (2013). Markov modelling for random dynamical systems. In Equadiff 99. https://doi.org/10.1142/9789812792617_0200","ama":"Froyland G. Markov modelling for random dynamical systems. In: Equadiff 99. ; 2013. doi:10.1142/9789812792617_0200","chicago":"Froyland, Gary. “Markov Modelling for Random Dynamical Systems.” In Equadiff 99, 2013. https://doi.org/10.1142/9789812792617_0200."},"year":"2013","type":"book_chapter","date_updated":"2022-01-06T06:52:52Z","_id":"16599","doi":"10.1142/9789812792617_0200","author":[{"first_name":"Gary","full_name":"Froyland, Gary","last_name":"Froyland"}],"department":[{"_id":"101"}],"publication":"Equadiff 99","publication_identifier":{"isbn":["9789810243593","9789812792617"]},"publication_status":"published","status":"public","date_created":"2020-04-16T06:05:19Z","title":"Markov modelling for random dynamical systems","user_id":"15701"},{"title":"Markov state models from short non-equilibrium simulations—Analysis and correction of estimation bias","user_id":"81513","extern":"1","publication_identifier":{"issn":["0021-9606","1089-7690"]},"publication_status":"published","status":"public","date_created":"2021-04-30T16:55:31Z","author":[{"first_name":"Feliks","full_name":"Nüske, Feliks","orcid":"0000-0003-2444-7889","last_name":"Nüske","id":"81513"},{"last_name":"Wu","first_name":"Hao","full_name":"Wu, Hao"},{"full_name":"Prinz, Jan-Hendrik","first_name":"Jan-Hendrik","last_name":"Prinz"},{"last_name":"Wehmeyer","full_name":"Wehmeyer, Christoph","first_name":"Christoph"},{"last_name":"Clementi","first_name":"Cecilia","full_name":"Clementi, Cecilia"},{"first_name":"Frank","full_name":"Noé, Frank","last_name":"Noé"}],"department":[{"_id":"101"}],"publication":"The Journal of Chemical Physics","article_number":"094104","doi":"10.1063/1.4976518","date_updated":"2022-01-06T06:55:20Z","_id":"21938","year":"2017","type":"journal_article","citation":{"mla":"Nüske, Feliks, et al. “Markov State Models from Short Non-Equilibrium Simulations—Analysis and Correction of Estimation Bias.” The Journal of Chemical Physics, 094104, 2017, doi:10.1063/1.4976518.","bibtex":"@article{Nüske_Wu_Prinz_Wehmeyer_Clementi_Noé_2017, title={Markov state models from short non-equilibrium simulations—Analysis and correction of estimation bias}, DOI={10.1063/1.4976518}, number={094104}, journal={The Journal of Chemical Physics}, author={Nüske, Feliks and Wu, Hao and Prinz, Jan-Hendrik and Wehmeyer, Christoph and Clementi, Cecilia and Noé, Frank}, year={2017} }","ama":"Nüske F, Wu H, Prinz J-H, Wehmeyer C, Clementi C, Noé F. Markov state models from short non-equilibrium simulations—Analysis and correction of estimation bias. The Journal of Chemical Physics. 2017. doi:10.1063/1.4976518","apa":"Nüske, F., Wu, H., Prinz, J.-H., Wehmeyer, C., Clementi, C., & Noé, F. (2017). Markov state models from short non-equilibrium simulations—Analysis and correction of estimation bias. The Journal of Chemical Physics. https://doi.org/10.1063/1.4976518","chicago":"Nüske, Feliks, Hao Wu, Jan-Hendrik Prinz, Christoph Wehmeyer, Cecilia Clementi, and Frank Noé. “Markov State Models from Short Non-Equilibrium Simulations—Analysis and Correction of Estimation Bias.” The Journal of Chemical Physics, 2017. https://doi.org/10.1063/1.4976518.","ieee":"F. Nüske, H. Wu, J.-H. Prinz, C. Wehmeyer, C. Clementi, and F. Noé, “Markov state models from short non-equilibrium simulations—Analysis and correction of estimation bias,” The Journal of Chemical Physics, 2017.","short":"F. Nüske, H. Wu, J.-H. Prinz, C. Wehmeyer, C. Clementi, F. Noé, The Journal of Chemical Physics (2017)."},"language":[{"iso":"eng"}]},{"type":"book_chapter","year":"1992","citation":{"short":"M. Dellnitz, M. Golubitsky, I. Melbourne, in: Bifurcation and Symmetry, Basel, 1992.","ieee":"M. Dellnitz, M. Golubitsky, and I. Melbourne, “Mechanisms of Symmetry Creation,” in Bifurcation and Symmetry, Basel, 1992.","chicago":"Dellnitz, Michael, Martin Golubitsky, and Ian Melbourne. “Mechanisms of Symmetry Creation.” In Bifurcation and Symmetry. Basel, 1992. https://doi.org/10.1007/978-3-0348-7536-3_9.","apa":"Dellnitz, M., Golubitsky, M., & Melbourne, I. (1992). Mechanisms of Symmetry Creation. In Bifurcation and Symmetry. Basel. https://doi.org/10.1007/978-3-0348-7536-3_9","ama":"Dellnitz M, Golubitsky M, Melbourne I. Mechanisms of Symmetry Creation. In: Bifurcation and Symmetry. 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Under standard assumptions, we prove convergence of a subset of iterates to a quasi-stationary point and if constraint qualifications hold, then the limit point is also a KKT-point of the multi-objective problem.","lang":"eng"}],"external_id":{"arxiv":["2208.12094"]},"title":"Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients","user_id":"47427","publication":"arXiv:2208.12094","department":[{"_id":"101"},{"_id":"655"}],"author":[{"full_name":"Berkemeier, Manuel Bastian","first_name":"Manuel Bastian","id":"51701","last_name":"Berkemeier"},{"id":"47427","last_name":"Peitz","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian"}],"date_created":"2022-08-26T06:08:06Z","status":"public","date_updated":"2022-08-26T06:12:10Z","_id":"33150","oa":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2208.12094"}],"year":"2022","citation":{"short":"M.B. Berkemeier, S. Peitz, ArXiv:2208.12094 (2022).","ieee":"M. B. Berkemeier and S. Peitz, “Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients,” arXiv:2208.12094. 2022.","chicago":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region Filter Method for Nonlinear Constraints Using Inexact Gradients.” ArXiv:2208.12094, 2022.","apa":"Berkemeier, M. B., & Peitz, S. (2022). Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients. In arXiv:2208.12094.","ama":"Berkemeier MB, Peitz S. Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients. arXiv:220812094. 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Dellnitz and O. Schütze, “Multilevel Subdivision Techniques for Scalar Optimization Problems,” in Global Analysis of Nonlinear Dynamics, New York, NY, 2012.","short":"M. Dellnitz, O. Schütze, in: Global Analysis of Nonlinear Dynamics, New York, NY, 2012.","mla":"Dellnitz, Michael, and Oliver Schütze. “Multilevel Subdivision Techniques for Scalar Optimization Problems.” Global Analysis of Nonlinear Dynamics, 2012, doi:10.1007/978-1-4614-3128-2_10.","bibtex":"@inbook{Dellnitz_Schütze_2012, place={New York, NY}, title={Multilevel Subdivision Techniques for Scalar Optimization Problems}, DOI={10.1007/978-1-4614-3128-2_10}, booktitle={Global Analysis of Nonlinear Dynamics}, author={Dellnitz, Michael and Schütze, Oliver}, year={2012} }","chicago":"Dellnitz, Michael, and Oliver Schütze. “Multilevel Subdivision Techniques for Scalar Optimization Problems.” In Global Analysis of Nonlinear Dynamics. New York, NY, 2012. https://doi.org/10.1007/978-1-4614-3128-2_10.","ama":"Dellnitz M, Schütze O. 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In Procedia Technology (pp. 483–490). https://doi.org/10.1016/j.protcy.2016.08.061","ama":"Peitz S, Gräler M, Henke C, Molo MH, Dellnitz M, Trächtler A. Multiobjective Model Predictive Control of an Industrial Laundry. In: Procedia Technology. ; 2016:483-490. doi:10.1016/j.protcy.2016.08.061","chicago":"Peitz, Sebastian, Manuel Gräler, Christian Henke, Mirko Hessel-von Molo, Michael Dellnitz, and Ansgar Trächtler. “Multiobjective Model Predictive Control of an Industrial Laundry.” In Procedia Technology, 483–90, 2016. https://doi.org/10.1016/j.protcy.2016.08.061.","mla":"Peitz, Sebastian, et al. “Multiobjective Model Predictive Control of an Industrial Laundry.” Procedia Technology, 2016, pp. 483–90, doi:10.1016/j.protcy.2016.08.061.","bibtex":"@inproceedings{Peitz_Gräler_Henke_Molo_Dellnitz_Trächtler_2016, title={Multiobjective Model Predictive Control of an Industrial Laundry}, DOI={10.1016/j.protcy.2016.08.061}, booktitle={Procedia Technology}, author={Peitz, Sebastian and Gräler, Manuel and Henke, Christian and Molo, Mirko Hessel-von and Dellnitz, Michael and Trächtler, Ansgar}, year={2016}, pages={483–490} }"},"language":[{"iso":"eng"}],"doi":"10.1016/j.protcy.2016.08.061","date_updated":"2022-01-06T07:04:00Z","_id":"8759","publication_status":"published","publication_identifier":{"issn":["2212-0173"]},"date_created":"2019-03-29T13:35:59Z","status":"public","publication":"Procedia Technology","department":[{"_id":"101"}],"author":[{"orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian","id":"47427","last_name":"Peitz"},{"full_name":"Gräler, Manuel","first_name":"Manuel","last_name":"Gräler"},{"last_name":"Henke","full_name":"Henke, Christian","first_name":"Christian"},{"last_name":"Molo","first_name":"Mirko Hessel-von","full_name":"Molo, Mirko Hessel-von"},{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"},{"last_name":"Trächtler","first_name":"Ansgar","full_name":"Trächtler, Ansgar"}],"title":"Multiobjective Model Predictive Control of an Industrial Laundry","user_id":"47427","abstract":[{"lang":"eng","text":"In a wide range of applications, it is desirable to optimally control a system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a single optimal solution, the set of optimal compromises, the so-called Pareto set, has to be approximated. When it is not possible to compute the entire control trajectory in advance, for instance due to uncertainties or unforeseeable events, model predictive control methods can be applied to control the system during operation in real time. In this article, we present an algorithm for the solution of multiobjective model predictive control problems. In an offline scenario, it can be used to compute the entire set of optimal compromises whereas in a real time scenario, one optimal compromise is computed according to an operator's preference. The results are illustrated using the example of an industrial laundry. A logistics model of the laundry is developed and then utilized in the optimization routine. Results are presented for an offline as well as an online scenario."}]},{"series_title":"Mathematics in Industry","year":"2016","type":"conference","citation":{"ama":"Dellnitz M, Eckstein J, Flaßkamp K, et al. Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control. In: Progress in Industrial Mathematics at ECMI. Vol 22. Mathematics in Industry. Cham: Springer International Publishing; 2016:633-641. doi:10.1007/978-3-319-23413-7_87","apa":"Dellnitz, M., Eckstein, J., Flaßkamp, K., Friedel, P., Horenkamp, C., Köhler, U., … Tiemeyer, S. (2016). Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control. In Progress in Industrial Mathematics at ECMI (Vol. 22, pp. 633–641). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-23413-7_87","chicago":"Dellnitz, Michael, Julian Eckstein, Kathrin Flaßkamp, Patrick Friedel, Christian Horenkamp, Ulrich Köhler, Sina Ober-Blöbaum, Sebastian Peitz, and Sebastian Tiemeyer. “Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control.” In Progress in Industrial Mathematics at ECMI, 22:633–41. Mathematics in Industry. Cham: Springer International Publishing, 2016. https://doi.org/10.1007/978-3-319-23413-7_87.","bibtex":"@inproceedings{Dellnitz_Eckstein_Flaßkamp_Friedel_Horenkamp_Köhler_Ober-Blöbaum_Peitz_Tiemeyer_2016, place={Cham}, series={Mathematics in Industry}, title={Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control}, volume={22}, DOI={10.1007/978-3-319-23413-7_87}, booktitle={Progress in Industrial Mathematics at ECMI}, publisher={Springer International Publishing}, author={Dellnitz, Michael and Eckstein, Julian and Flaßkamp, Kathrin and Friedel, Patrick and Horenkamp, Christian and Köhler, Ulrich and Ober-Blöbaum, Sina and Peitz, Sebastian and Tiemeyer, Sebastian}, year={2016}, pages={633–641}, collection={Mathematics in Industry} }","mla":"Dellnitz, Michael, et al. “Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control.” Progress in Industrial Mathematics at ECMI, vol. 22, Springer International Publishing, 2016, pp. 633–41, doi:10.1007/978-3-319-23413-7_87.","short":"M. Dellnitz, J. Eckstein, K. Flaßkamp, P. Friedel, C. Horenkamp, U. Köhler, S. Ober-Blöbaum, S. Peitz, S. Tiemeyer, in: Progress in Industrial Mathematics at ECMI, Springer International Publishing, Cham, 2016, pp. 633–641.","ieee":"M. Dellnitz et al., “Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control,” in Progress in Industrial Mathematics at ECMI, 2016, vol. 22, pp. 633–641."},"page":"633-641","date_updated":"2022-01-06T06:59:14Z","_id":"34","intvolume":" 22","doi":"10.1007/978-3-319-23413-7_87","publisher":"Springer International Publishing","author":[{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"},{"last_name":"Eckstein","full_name":"Eckstein, Julian","first_name":"Julian"},{"last_name":"Flaßkamp","full_name":"Flaßkamp, Kathrin","first_name":"Kathrin"},{"first_name":"Patrick","full_name":"Friedel, Patrick","last_name":"Friedel"},{"full_name":"Horenkamp, Christian","first_name":"Christian","last_name":"Horenkamp"},{"full_name":"Köhler, Ulrich","first_name":"Ulrich","last_name":"Köhler"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","last_name":"Peitz"},{"first_name":"Sebastian","full_name":"Tiemeyer, Sebastian","last_name":"Tiemeyer"}],"publication":"Progress in Industrial Mathematics at ECMI","department":[{"_id":"27"},{"_id":"101"}],"publication_identifier":{"issn":["2212-0173"]},"volume":22,"status":"public","date_created":"2017-07-26T15:25:33Z","place":"Cham","title":"Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control","user_id":"24135"},{"place":"Cham","title":"Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control","user_id":"15701","publication":"Mathematics in Industry","department":[{"_id":"101"}],"author":[{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"},{"last_name":"Eckstein","first_name":"Julian","full_name":"Eckstein, Julian"},{"first_name":"Kathrin","full_name":"Flaßkamp, Kathrin","last_name":"Flaßkamp"},{"last_name":"Friedel","full_name":"Friedel, Patrick","first_name":"Patrick"},{"first_name":"Christian","full_name":"Horenkamp, Christian","last_name":"Horenkamp"},{"first_name":"Ulrich","full_name":"Köhler, Ulrich","last_name":"Köhler"},{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"last_name":"Peitz","full_name":"Peitz, Sebastian","first_name":"Sebastian"},{"last_name":"Tiemeyer","first_name":"Sebastian","full_name":"Tiemeyer, Sebastian"}],"publication_status":"published","publication_identifier":{"isbn":["9783319234120","9783319234137"],"issn":["1612-3956","2198-3283"]},"date_created":"2020-04-16T05:37:11Z","status":"public","_id":"16579","date_updated":"2022-01-06T06:52:52Z","doi":"10.1007/978-3-319-23413-7_87","year":"2016","type":"book_chapter","citation":{"ieee":"M. Dellnitz et al., “Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control,” in Mathematics in Industry, Cham, 2016.","short":"M. Dellnitz, J. Eckstein, K. Flaßkamp, P. Friedel, C. Horenkamp, U. Köhler, S. Ober-Blöbaum, S. Peitz, S. Tiemeyer, in: Mathematics in Industry, Cham, 2016.","bibtex":"@inbook{Dellnitz_Eckstein_Flaßkamp_Friedel_Horenkamp_Köhler_Ober-Blöbaum_Peitz_Tiemeyer_2016, place={Cham}, title={Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control}, DOI={10.1007/978-3-319-23413-7_87}, booktitle={Mathematics in Industry}, author={Dellnitz, Michael and Eckstein, Julian and Flaßkamp, Kathrin and Friedel, Patrick and Horenkamp, Christian and Köhler, Ulrich and Ober-Blöbaum, Sina and Peitz, Sebastian and Tiemeyer, Sebastian}, year={2016} }","mla":"Dellnitz, Michael, et al. “Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control.” Mathematics in Industry, 2016, doi:10.1007/978-3-319-23413-7_87.","ama":"Dellnitz M, Eckstein J, Flaßkamp K, et al. Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control. In: Mathematics in Industry. Cham; 2016. doi:10.1007/978-3-319-23413-7_87","apa":"Dellnitz, M., Eckstein, J., Flaßkamp, K., Friedel, P., Horenkamp, C., Köhler, U., … Tiemeyer, S. (2016). Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control. In Mathematics in Industry. Cham. https://doi.org/10.1007/978-3-319-23413-7_87","chicago":"Dellnitz, Michael, Julian Eckstein, Kathrin Flaßkamp, Patrick Friedel, Christian Horenkamp, Ulrich Köhler, Sina Ober-Blöbaum, Sebastian Peitz, and Sebastian Tiemeyer. “Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control.” In Mathematics in Industry. Cham, 2016. https://doi.org/10.1007/978-3-319-23413-7_87."},"language":[{"iso":"eng"}]},{"date_updated":"2022-01-21T10:01:41Z","doi":"10.1007/s10440-018-0209-7","language":[{"iso":"eng"}],"title":"Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling","department":[{"_id":"101"}],"project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"publication_identifier":{"issn":["0167-8019","1572-9036"]},"publication_status":"published","intvolume":" 161","_id":"8753","issue":"1","page":"171–199","type":"journal_article","citation":{"short":"S. Peitz, S. Ober-Blöbaum, M. Dellnitz, Acta Applicandae Mathematicae 161 (2018) 171–199.","ieee":"S. Peitz, S. Ober-Blöbaum, and M. Dellnitz, “Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling,” Acta Applicandae Mathematicae, vol. 161, no. 1, pp. 171–199, 2018, doi: 10.1007/s10440-018-0209-7.","apa":"Peitz, S., Ober-Blöbaum, S., & Dellnitz, M. (2018). Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling. Acta Applicandae Mathematicae, 161(1), 171–199. https://doi.org/10.1007/s10440-018-0209-7","ama":"Peitz S, Ober-Blöbaum S, Dellnitz M. Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling. Acta Applicandae Mathematicae. 2018;161(1):171–199. doi:10.1007/s10440-018-0209-7","chicago":"Peitz, Sebastian, Sina Ober-Blöbaum, and Michael Dellnitz. “Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling.” Acta Applicandae Mathematicae 161, no. 1 (2018): 171–199. https://doi.org/10.1007/s10440-018-0209-7.","mla":"Peitz, Sebastian, et al. “Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling.” Acta Applicandae Mathematicae, vol. 161, no. 1, 2018, pp. 171–199, doi:10.1007/s10440-018-0209-7.","bibtex":"@article{Peitz_Ober-Blöbaum_Dellnitz_2018, title={Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling}, volume={161}, DOI={10.1007/s10440-018-0209-7}, number={1}, journal={Acta Applicandae Mathematicae}, author={Peitz, Sebastian and Ober-Blöbaum, Sina and Dellnitz, Michael}, year={2018}, pages={171–199} }"},"year":"2018","abstract":[{"text":"In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a single optimal solution, the set of optimal compromises, the so-called Pareto set, has to be approximated. When the problem under consideration is described by a partial differential equation (PDE), as is the case for fluid flow, the computational cost rapidly increases and makes its direct treatment infeasible. Reduced order modeling is a very popular method to reduce the computational cost, in particular in a multi query context such as uncertainty quantification, parameter estimation or optimization. In this article, we show how to combine reduced order modeling and multiobjective optimal control techniques in order to efficiently solve multiobjective optimal control problems constrained by PDEs. We consider a global, derivative free optimization method as well as a local, gradient-based approach for which the optimality system is derived in two different ways. The methods are compared with regard to the solution quality as well as the computational effort and they are illustrated using the example of the flow around a cylinder and a backward-facing-step channel flow.","lang":"eng"}],"user_id":"15694","publication":"Acta Applicandae Mathematicae","author":[{"orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian","id":"47427","last_name":"Peitz"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","id":"16494"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"}],"date_created":"2019-03-29T13:30:41Z","status":"public","volume":161},{"department":[{"_id":"101"}],"publication":"PAMM","author":[{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"},{"first_name":"Kathrin","full_name":"Padberg-Gehle, Kathrin","last_name":"Padberg-Gehle"}],"publication_status":"published","publication_identifier":{"issn":["1617-7061"]},"date_created":"2020-04-16T09:00:48Z","status":"public","title":"Multiobjective optimal control of fluid mixing","user_id":"15701","page":"639-640","type":"journal_article","citation":{"chicago":"Ober-Blöbaum, Sina, and Kathrin Padberg-Gehle. “Multiobjective Optimal Control of Fluid Mixing.” PAMM, 2015, 639–40. https://doi.org/10.1002/pamm.201510309.","apa":"Ober-Blöbaum, S., & Padberg-Gehle, K. (2015). Multiobjective optimal control of fluid mixing. PAMM, 639–640. https://doi.org/10.1002/pamm.201510309","ama":"Ober-Blöbaum S, Padberg-Gehle K. Multiobjective optimal control of fluid mixing. PAMM. 2015:639-640. doi:10.1002/pamm.201510309","mla":"Ober-Blöbaum, Sina, and Kathrin Padberg-Gehle. “Multiobjective Optimal Control of Fluid Mixing.” PAMM, 2015, pp. 639–40, doi:10.1002/pamm.201510309.","bibtex":"@article{Ober-Blöbaum_Padberg-Gehle_2015, title={Multiobjective optimal control of fluid mixing}, DOI={10.1002/pamm.201510309}, journal={PAMM}, author={Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}, year={2015}, pages={639–640} }","short":"S. Ober-Blöbaum, K. Padberg-Gehle, PAMM (2015) 639–640.","ieee":"S. Ober-Blöbaum and K. Padberg-Gehle, “Multiobjective optimal control of fluid mixing,” PAMM, pp. 639–640, 2015."},"year":"2015","language":[{"iso":"eng"}],"date_updated":"2022-01-06T06:52:53Z","_id":"16642","doi":"10.1002/pamm.201510309"},{"user_id":"15701","title":"Multiobjective optimization for transistor sizing of CMOS logic standard cells using set-oriented numerical techniques","status":"public","date_created":"2020-04-15T08:11:10Z","publication_identifier":{"isbn":["9781424443109","9781424443116"]},"publication_status":"published","author":[{"last_name":"Blesken","full_name":"Blesken, Matthias","first_name":"Matthias"},{"last_name":"Ruckert","first_name":"Ulrich","full_name":"Ruckert, Ulrich"},{"last_name":"Steenken","first_name":"Dominik","full_name":"Steenken, Dominik"},{"last_name":"Witting","first_name":"Katrin","full_name":"Witting, Katrin"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"}],"department":[{"_id":"101"}],"publication":"2009 NORCHIP","doi":"10.1109/norchp.2009.5397800","date_updated":"2022-01-06T06:52:52Z","_id":"16524","language":[{"iso":"eng"}],"year":"2009","citation":{"short":"M. Blesken, U. Ruckert, D. Steenken, K. Witting, M. Dellnitz, in: 2009 NORCHIP, 2009.","ieee":"M. Blesken, U. Ruckert, D. Steenken, K. Witting, and M. Dellnitz, “Multiobjective optimization for transistor sizing of CMOS logic standard cells using set-oriented numerical techniques,” in 2009 NORCHIP, 2009.","ama":"Blesken M, Ruckert U, Steenken D, Witting K, Dellnitz M. Multiobjective optimization for transistor sizing of CMOS logic standard cells using set-oriented numerical techniques. In: 2009 NORCHIP. ; 2009. doi:10.1109/norchp.2009.5397800","apa":"Blesken, M., Ruckert, U., Steenken, D., Witting, K., & Dellnitz, M. (2009). Multiobjective optimization for transistor sizing of CMOS logic standard cells using set-oriented numerical techniques. In 2009 NORCHIP. https://doi.org/10.1109/norchp.2009.5397800","chicago":"Blesken, Matthias, Ulrich Ruckert, Dominik Steenken, Katrin Witting, and Michael Dellnitz. “Multiobjective Optimization for Transistor Sizing of CMOS Logic Standard Cells Using Set-Oriented Numerical Techniques.” In 2009 NORCHIP, 2009. https://doi.org/10.1109/norchp.2009.5397800.","bibtex":"@inproceedings{Blesken_Ruckert_Steenken_Witting_Dellnitz_2009, title={Multiobjective optimization for transistor sizing of CMOS logic standard cells using set-oriented numerical techniques}, DOI={10.1109/norchp.2009.5397800}, booktitle={2009 NORCHIP}, author={Blesken, Matthias and Ruckert, Ulrich and Steenken, Dominik and Witting, Katrin and Dellnitz, Michael}, year={2009} }","mla":"Blesken, Matthias, et al. “Multiobjective Optimization for Transistor Sizing of CMOS Logic Standard Cells Using Set-Oriented Numerical Techniques.” 2009 NORCHIP, 2009, doi:10.1109/norchp.2009.5397800."},"type":"conference"},{"user_id":"15701","title":"Multiobjective Optimization of Control Trajectories for the Guidance of a Rail-bound Vehicle","department":[{"_id":"101"}],"publication":"IFAC Proceedings Volumes","author":[{"first_name":"M.Sc. Jens","full_name":"Geisler, M.Sc. Jens","last_name":"Geisler"},{"full_name":"Witting, Dipl.-Math. Katrin","first_name":"Dipl.-Math. Katrin","last_name":"Witting"},{"last_name":"Trächtler","full_name":"Trächtler, Ansgar","first_name":"Ansgar"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"date_created":"2020-04-16T08:01:27Z","status":"public","publication_status":"published","publication_identifier":{"issn":["1474-6670"]},"_id":"16610","date_updated":"2022-01-06T06:52:53Z","doi":"10.3182/20080706-5-kr-1001.00738","language":[{"iso":"eng"}],"page":"4380-4386","citation":{"ieee":"M. S. J. Geisler, D.-M. K. Witting, A. Trächtler, and M. Dellnitz, “Multiobjective Optimization of Control Trajectories for the Guidance of a Rail-bound Vehicle,” IFAC Proceedings Volumes, pp. 4380–4386, 2008.","short":"M.S.J. Geisler, D.-M.K. Witting, A. Trächtler, M. Dellnitz, IFAC Proceedings Volumes (2008) 4380–4386.","mla":"Geisler, M. Sc. Jens, et al. “Multiobjective Optimization of Control Trajectories for the Guidance of a Rail-Bound Vehicle.” IFAC Proceedings Volumes, 2008, pp. 4380–86, doi:10.3182/20080706-5-kr-1001.00738.","bibtex":"@article{Geisler_Witting_Trächtler_Dellnitz_2008, title={Multiobjective Optimization of Control Trajectories for the Guidance of a Rail-bound Vehicle}, DOI={10.3182/20080706-5-kr-1001.00738}, journal={IFAC Proceedings Volumes}, author={Geisler, M.Sc. Jens and Witting, Dipl.-Math. Katrin and Trächtler, Ansgar and Dellnitz, Michael}, year={2008}, pages={4380–4386} }","apa":"Geisler, M. S. J., Witting, D.-M. K., Trächtler, A., & Dellnitz, M. (2008). Multiobjective Optimization of Control Trajectories for the Guidance of a Rail-bound Vehicle. IFAC Proceedings Volumes, 4380–4386. https://doi.org/10.3182/20080706-5-kr-1001.00738","ama":"Geisler MSJ, Witting D-MK, Trächtler A, Dellnitz M. Multiobjective Optimization of Control Trajectories for the Guidance of a Rail-bound Vehicle. IFAC Proceedings Volumes. 2008:4380-4386. doi:10.3182/20080706-5-kr-1001.00738","chicago":"Geisler, M.Sc. Jens, Dipl.-Math. Katrin Witting, Ansgar Trächtler, and Michael Dellnitz. “Multiobjective Optimization of Control Trajectories for the Guidance of a Rail-Bound Vehicle.” IFAC Proceedings Volumes, 2008, 4380–86. https://doi.org/10.3182/20080706-5-kr-1001.00738."},"type":"journal_article","year":"2008"},{"oa":"1","date_updated":"2024-02-21T12:22:20Z","_id":"46578","language":[{"iso":"eng"}],"type":"preprint","year":"2023","citation":{"chicago":"Bernreuther, Marco, Michael Dellnitz, Bennet Gebken, Georg Müller, Sebastian Peitz, Konstantin Sonntag, and Stefan Volkwein. “Multiobjective Optimization of Non-Smooth PDE-Constrained Problems.” ArXiv:2308.01113, 2023.","apa":"Bernreuther, M., Dellnitz, M., Gebken, B., Müller, G., Peitz, S., Sonntag, K., & Volkwein, S. (2023). Multiobjective Optimization of Non-Smooth PDE-Constrained Problems. In arXiv:2308.01113.","ama":"Bernreuther M, Dellnitz M, Gebken B, et al. Multiobjective Optimization of Non-Smooth PDE-Constrained Problems. arXiv:230801113. Published online 2023.","mla":"Bernreuther, Marco, et al. “Multiobjective Optimization of Non-Smooth PDE-Constrained Problems.” ArXiv:2308.01113, 2023.","bibtex":"@article{Bernreuther_Dellnitz_Gebken_Müller_Peitz_Sonntag_Volkwein_2023, title={Multiobjective Optimization of Non-Smooth PDE-Constrained Problems}, journal={arXiv:2308.01113}, author={Bernreuther, Marco and Dellnitz, Michael and Gebken, Bennet and Müller, Georg and Peitz, Sebastian and Sonntag, Konstantin and Volkwein, Stefan}, year={2023} }","short":"M. Bernreuther, M. Dellnitz, B. Gebken, G. Müller, S. Peitz, K. Sonntag, S. Volkwein, ArXiv:2308.01113 (2023).","ieee":"M. Bernreuther et al., “Multiobjective Optimization of Non-Smooth PDE-Constrained Problems,” arXiv:2308.01113. 2023."},"main_file_link":[{"url":"https://arxiv.org/pdf/2308.01113","open_access":"1"}],"user_id":"47427","title":"Multiobjective Optimization of Non-Smooth PDE-Constrained Problems","external_id":{"arxiv":["2308.01113"]},"abstract":[{"text":"Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control - potentially with non-smoothness both on the level of the objectives or in the system dynamics. This results in new challenges such as dealing with expensive models (e.g., governed by partial differential equations (PDEs)) and developing dedicated algorithms handling the non-smoothness. Since in contrast to single-objective optimization, the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in the field of multiobjective optimization of non-smooth PDE-constrained problems. In particular we report on the advances achieved within Project 2 \"Multiobjective Optimization of Non-Smooth PDE-Constrained Problems - Switches, State Constraints and Model Order Reduction\" of the DFG Priority Programm 1962 \"Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization\".","lang":"eng"}],"date_created":"2023-08-21T05:50:12Z","status":"public","department":[{"_id":"655"},{"_id":"101"}],"publication":"arXiv:2308.01113","author":[{"first_name":"Marco","full_name":"Bernreuther, Marco","last_name":"Bernreuther"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"full_name":"Gebken, Bennet","first_name":"Bennet","id":"32643","last_name":"Gebken"},{"last_name":"Müller","full_name":"Müller, Georg","first_name":"Georg"},{"last_name":"Peitz","id":"47427","first_name":"Sebastian","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian"},{"full_name":"Sonntag, Konstantin","orcid":"https://orcid.org/0000-0003-3384-3496","first_name":"Konstantin","id":"56399","last_name":"Sonntag"},{"first_name":"Stefan","full_name":"Volkwein, Stefan","last_name":"Volkwein"}]},{"user_id":"24135","title":"Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction","abstract":[{"text":"In this article an efficient numerical method to solve multiobjective optimization problems for fluid flow governed by the Navier Stokes equations is presented. In order to decrease the computational effort, a reduced order model is introduced using Proper Orthogonal Decomposition and a corresponding Galerkin Projection. A global, derivative free multiobjective optimization algorithm is applied to compute the Pareto set (i.e. the set of optimal compromises) for the concurrent objectives minimization of flow field fluctuations and control cost. The method is illustrated for a 2D flow around a cylinder at Re = 100.","lang":"eng"}],"date_created":"2018-03-23T14:14:24Z","status":"public","volume":15,"publication_identifier":{"issn":["1617-7061"]},"publication":"PAMM","department":[{"_id":"27"},{"_id":"101"}],"author":[{"full_name":"Peitz, Sebastian","first_name":"Sebastian","last_name":"Peitz"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"}],"publisher":"WILEY-VCH Verlag","issue":"1","doi":"10.1002/pamm.201510296","_id":"1774","date_updated":"2022-01-06T06:53:19Z","intvolume":" 15","page":"613-614","citation":{"chicago":"Peitz, Sebastian, and Michael Dellnitz. “Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction.” PAMM 15, no. 1 (2015): 613–14. https://doi.org/10.1002/pamm.201510296.","ama":"Peitz S, Dellnitz M. Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction. PAMM. 2015;15(1):613-614. doi:10.1002/pamm.201510296","apa":"Peitz, S., & Dellnitz, M. (2015). Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction. PAMM, 15(1), 613–614. https://doi.org/10.1002/pamm.201510296","bibtex":"@article{Peitz_Dellnitz_2015, title={Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction}, volume={15}, DOI={10.1002/pamm.201510296}, number={1}, journal={PAMM}, publisher={WILEY-VCH Verlag}, author={Peitz, Sebastian and Dellnitz, Michael}, year={2015}, pages={613–614} }","mla":"Peitz, Sebastian, and Michael Dellnitz. “Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction.” PAMM, vol. 15, no. 1, WILEY-VCH Verlag, 2015, pp. 613–14, doi:10.1002/pamm.201510296.","short":"S. Peitz, M. Dellnitz, PAMM 15 (2015) 613–614.","ieee":"S. Peitz and M. Dellnitz, “Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction,” PAMM, vol. 15, no. 1, pp. 613–614, 2015."},"year":"2015","type":"journal_article"},{"date_updated":"2022-01-06T07:04:00Z","_id":"8760","doi":"10.1002/pamm.201510296","language":[{"iso":"eng"}],"page":"613-614","citation":{"bibtex":"@inproceedings{Peitz_Dellnitz_2015, title={Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction}, DOI={10.1002/pamm.201510296}, booktitle={PAMM}, author={Peitz, Sebastian and Dellnitz, Michael}, year={2015}, pages={613–614} }","mla":"Peitz, Sebastian, and Michael Dellnitz. “Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction.” PAMM, 2015, pp. 613–14, doi:10.1002/pamm.201510296.","chicago":"Peitz, Sebastian, and Michael Dellnitz. “Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction.” In PAMM, 613–14, 2015. https://doi.org/10.1002/pamm.201510296.","ama":"Peitz S, Dellnitz M. Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction. In: PAMM. ; 2015:613-614. doi:10.1002/pamm.201510296","apa":"Peitz, S., & Dellnitz, M. (2015). Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction. In PAMM (pp. 613–614). https://doi.org/10.1002/pamm.201510296","ieee":"S. Peitz and M. Dellnitz, “Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction,” in PAMM, 2015, pp. 613–614.","short":"S. Peitz, M. Dellnitz, in: PAMM, 2015, pp. 613–614."},"year":"2015","type":"conference","abstract":[{"text":"n this article an efficient numerical method to solve multiobjective optimization problems for fluid flow governed by the Navier Stokes equations is presented. In order to decrease the computational effort, a reduced order model is introduced using Proper Orthogonal Decomposition and a corresponding Galerkin Projection. A global, derivative free multiobjective optimization algorithm is applied to compute the Pareto set (i.e. the set of optimal compromises) for the concurrent objectives minimization of flow field fluctuations and control cost. The method is illustrated for a 2D flow around a cylinder at Re = 100.","lang":"eng"}],"user_id":"47427","title":"Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction","department":[{"_id":"101"}],"publication":"PAMM","author":[{"last_name":"Peitz","id":"47427","first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"}],"date_created":"2019-03-29T13:36:33Z","status":"public","publication_status":"published","publication_identifier":{"issn":["1617-7061"]}},{"language":[{"iso":"eng"}],"type":"journal_article","citation":{"ieee":"S. Bezrukov, R. Elsässer, B. Monien, R. Preis, and J.-P. Tillich, “New spectral lower bounds on the bisection width of graphs,” Theoretical Computer Science, pp. 155–174, 2004.","short":"S. Bezrukov, R. Elsässer, B. Monien, R. Preis, J.-P. Tillich, Theoretical Computer Science (2004) 155–174.","bibtex":"@article{Bezrukov_Elsässer_Monien_Preis_Tillich_2004, title={New spectral lower bounds on the bisection width of graphs}, DOI={10.1016/j.tcs.2004.03.059}, journal={Theoretical Computer Science}, author={Bezrukov, S. and Elsässer, R. and Monien, B. and Preis, R. and Tillich, J.-P.}, year={2004}, pages={155–174} }","mla":"Bezrukov, S., et al. “New Spectral Lower Bounds on the Bisection Width of Graphs.” Theoretical Computer Science, 2004, pp. 155–74, doi:10.1016/j.tcs.2004.03.059.","ama":"Bezrukov S, Elsässer R, Monien B, Preis R, Tillich J-P. New spectral lower bounds on the bisection width of graphs. Theoretical Computer Science. 2004:155-174. doi:10.1016/j.tcs.2004.03.059","apa":"Bezrukov, S., Elsässer, R., Monien, B., Preis, R., & Tillich, J.-P. (2004). New spectral lower bounds on the bisection width of graphs. Theoretical Computer Science, 155–174. https://doi.org/10.1016/j.tcs.2004.03.059","chicago":"Bezrukov, S., R. Elsässer, B. Monien, R. Preis, and J.-P. Tillich. “New Spectral Lower Bounds on the Bisection Width of Graphs.” Theoretical Computer Science, 2004, 155–74. https://doi.org/10.1016/j.tcs.2004.03.059."},"year":"2004","page":"155-174","_id":"16521","date_updated":"2022-01-06T06:52:52Z","doi":"10.1016/j.tcs.2004.03.059","author":[{"last_name":"Bezrukov","first_name":"S.","full_name":"Bezrukov, S."},{"first_name":"R.","full_name":"Elsässer, R.","last_name":"Elsässer"},{"first_name":"B.","full_name":"Monien, B.","last_name":"Monien"},{"last_name":"Preis","full_name":"Preis, R.","first_name":"R."},{"first_name":"J.-P.","full_name":"Tillich, J.-P.","last_name":"Tillich"}],"publication":"Theoretical Computer Science","department":[{"_id":"101"}],"status":"public","date_created":"2020-04-15T08:05:40Z","publication_identifier":{"issn":["0304-3975"]},"publication_status":"published","user_id":"15701","title":"New spectral lower bounds on the bisection width of graphs"},{"publication_identifier":{"isbn":["9783642298424","9783642298431"],"issn":["0302-9743","1611-3349"]},"publication_status":"published","date_created":"2020-04-15T07:59:49Z","status":"public","publication":"Large-Scale Scientific Computing","department":[{"_id":"101"}],"author":[{"full_name":"Baier, Robert","first_name":"Robert","last_name":"Baier"},{"full_name":"Molo, Mirko Hessel-von","first_name":"Mirko Hessel-von","last_name":"Molo"}],"title":"Newton’s Method and Secant Method for Set-Valued Mappings","user_id":"15701","place":"Berlin, Heidelberg","year":"2012","citation":{"bibtex":"@inbook{Baier_Molo_2012, place={Berlin, Heidelberg}, title={Newton’s Method and Secant Method for Set-Valued Mappings}, DOI={10.1007/978-3-642-29843-1_9}, booktitle={Large-Scale Scientific Computing}, author={Baier, Robert and Molo, Mirko Hessel-von}, year={2012} }","mla":"Baier, Robert, and Mirko Hessel-von Molo. “Newton’s Method and Secant Method for Set-Valued Mappings.” Large-Scale Scientific Computing, 2012, doi:10.1007/978-3-642-29843-1_9.","apa":"Baier, R., & Molo, M. H. (2012). Newton’s Method and Secant Method for Set-Valued Mappings. In Large-Scale Scientific Computing. Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_9","ama":"Baier R, Molo MH. Newton’s Method and Secant Method for Set-Valued Mappings. In: Large-Scale Scientific Computing. Berlin, Heidelberg; 2012. doi:10.1007/978-3-642-29843-1_9","chicago":"Baier, Robert, and Mirko Hessel-von Molo. “Newton’s Method and Secant Method for Set-Valued Mappings.” In Large-Scale Scientific Computing. Berlin, Heidelberg, 2012. https://doi.org/10.1007/978-3-642-29843-1_9.","ieee":"R. Baier and M. H. Molo, “Newton’s Method and Secant Method for Set-Valued Mappings,” in Large-Scale Scientific Computing, Berlin, Heidelberg, 2012.","short":"R. Baier, M.H. Molo, in: Large-Scale Scientific Computing, Berlin, Heidelberg, 2012."},"type":"book_chapter","doi":"10.1007/978-3-642-29843-1_9","date_updated":"2022-01-06T06:52:52Z","_id":"16516"},{"page":"235-268","citation":{"bibtex":"@article{Melbourne_Dellnitz_1993, title={Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group}, DOI={10.1017/s0305004100071577}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, author={Melbourne, Ian and Dellnitz, Michael}, year={1993}, pages={235–268} }","mla":"Melbourne, Ian, and Michael Dellnitz. “Normal Forms for Linear Hamiltonian Vector Fields Commuting with the Action of a Compact Lie Group.” Mathematical Proceedings of the Cambridge Philosophical Society, 1993, pp. 235–68, doi:10.1017/s0305004100071577.","chicago":"Melbourne, Ian, and Michael Dellnitz. “Normal Forms for Linear Hamiltonian Vector Fields Commuting with the Action of a Compact Lie Group.” Mathematical Proceedings of the Cambridge Philosophical Society, 1993, 235–68. https://doi.org/10.1017/s0305004100071577.","apa":"Melbourne, I., & Dellnitz, M. (1993). Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group. Mathematical Proceedings of the Cambridge Philosophical Society, 235–268. https://doi.org/10.1017/s0305004100071577","ama":"Melbourne I, Dellnitz M. Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group. Mathematical Proceedings of the Cambridge Philosophical Society. 1993:235-268. doi:10.1017/s0305004100071577","ieee":"I. Melbourne and M. Dellnitz, “Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group,” Mathematical Proceedings of the Cambridge Philosophical Society, pp. 235–268, 1993.","short":"I. Melbourne, M. Dellnitz, Mathematical Proceedings of the Cambridge Philosophical Society (1993) 235–268."},"type":"journal_article","year":"1993","language":[{"iso":"eng"}],"doi":"10.1017/s0305004100071577","date_updated":"2022-01-06T06:52:53Z","_id":"16633","publication_identifier":{"issn":["0305-0041","1469-8064"]},"publication_status":"published","date_created":"2020-04-16T08:31:40Z","status":"public","publication":"Mathematical Proceedings of the Cambridge Philosophical Society","department":[{"_id":"101"}],"author":[{"last_name":"Melbourne","first_name":"Ian","full_name":"Melbourne, Ian"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"}],"title":"Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group","user_id":"15701","abstract":[{"lang":"eng","text":"AbstractWe obtain normal forms for infinitesimally symplectic matrices (or linear Hamiltonian vector fields) that commute with the symplectic action of a compact Lie group of symmetries. In doing so we extend Williamson's theorem on normal forms when there is no symmetry present.Using standard representation-theoretic results the symmetry can be factored out and we reduce to finding normal forms over a real division ring. There are three real division rings consisting of the real, complex and quaternionic numbers. Of these, only the real case is covered in Williamson's original work."}]},{"year":"2006","citation":{"chicago":"Dellnitz, Michael, Oliver Junge, Marcus Post, and Bianca Thiere. “On Target for Venus – Set Oriented Computation of Energy Efficient Low Thrust Trajectories.” Celestial Mechanics and Dynamical Astronomy, 2006, 357–70. https://doi.org/10.1007/s10569-006-9008-y.","apa":"Dellnitz, M., Junge, O., Post, M., & Thiere, B. (2006). On target for Venus – set oriented computation of energy efficient low thrust trajectories. Celestial Mechanics and Dynamical Astronomy, 357–370. https://doi.org/10.1007/s10569-006-9008-y","ama":"Dellnitz M, Junge O, Post M, Thiere B. On target for Venus – set oriented computation of energy efficient low thrust trajectories. Celestial Mechanics and Dynamical Astronomy. 2006:357-370. doi:10.1007/s10569-006-9008-y","mla":"Dellnitz, Michael, et al. “On Target for Venus – Set Oriented Computation of Energy Efficient Low Thrust Trajectories.” Celestial Mechanics and Dynamical Astronomy, 2006, pp. 357–70, doi:10.1007/s10569-006-9008-y.","bibtex":"@article{Dellnitz_Junge_Post_Thiere_2006, title={On target for Venus – set oriented computation of energy efficient low thrust trajectories}, DOI={10.1007/s10569-006-9008-y}, journal={Celestial Mechanics and Dynamical Astronomy}, author={Dellnitz, Michael and Junge, Oliver and Post, Marcus and Thiere, Bianca}, year={2006}, pages={357–370} }","short":"M. Dellnitz, O. Junge, M. Post, B. Thiere, Celestial Mechanics and Dynamical Astronomy (2006) 357–370.","ieee":"M. Dellnitz, O. Junge, M. Post, and B. Thiere, “On target for Venus – set oriented computation of energy efficient low thrust trajectories,” Celestial Mechanics and Dynamical Astronomy, pp. 357–370, 2006."},"type":"journal_article","page":"357-370","language":[{"iso":"eng"}],"doi":"10.1007/s10569-006-9008-y","date_updated":"2022-01-06T06:52:52Z","_id":"16560","publication_status":"published","publication_identifier":{"issn":["0923-2958","1572-9478"]},"status":"public","date_created":"2020-04-15T09:58:17Z","author":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"full_name":"Junge, Oliver","first_name":"Oliver","last_name":"Junge"},{"last_name":"Post","full_name":"Post, Marcus","first_name":"Marcus"},{"last_name":"Thiere","first_name":"Bianca","full_name":"Thiere, Bianca"}],"department":[{"_id":"101"}],"publication":"Celestial Mechanics and Dynamical Astronomy","title":"On target for Venus – set oriented computation of energy efficient low thrust trajectories","user_id":"15701"},{"language":[{"iso":"eng"}],"citation":{"ieee":"M. Dellnitz and O. Junge, “On the Approximation of Complicated Dynamical Behavior,” SIAM Journal on Numerical Analysis, pp. 491–515, 1999.","short":"M. Dellnitz, O. Junge, SIAM Journal on Numerical Analysis (1999) 491–515.","mla":"Dellnitz, Michael, and Oliver Junge. “On the Approximation of Complicated Dynamical Behavior.” SIAM Journal on Numerical Analysis, 1999, pp. 491–515, doi:10.1137/s0036142996313002.","bibtex":"@article{Dellnitz_Junge_1999, title={On the Approximation of Complicated Dynamical Behavior}, DOI={10.1137/s0036142996313002}, journal={SIAM Journal on Numerical Analysis}, author={Dellnitz, Michael and Junge, Oliver}, year={1999}, pages={491–515} }","chicago":"Dellnitz, Michael, and Oliver Junge. “On the Approximation of Complicated Dynamical Behavior.” SIAM Journal on Numerical Analysis, 1999, 491–515. https://doi.org/10.1137/s0036142996313002.","ama":"Dellnitz M, Junge O. On the Approximation of Complicated Dynamical Behavior. SIAM Journal on Numerical Analysis. 1999:491-515. doi:10.1137/s0036142996313002","apa":"Dellnitz, M., & Junge, O. (1999). On the Approximation of Complicated Dynamical Behavior. SIAM Journal on Numerical Analysis, 491–515. https://doi.org/10.1137/s0036142996313002"},"year":"1999","type":"journal_article","page":"491-515","_id":"16537","date_updated":"2022-01-06T06:52:52Z","doi":"10.1137/s0036142996313002","author":[{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"},{"first_name":"Oliver","full_name":"Junge, Oliver","last_name":"Junge"}],"department":[{"_id":"101"}],"publication":"SIAM Journal on Numerical Analysis","status":"public","date_created":"2020-04-15T08:35:45Z","publication_status":"published","publication_identifier":{"issn":["0036-1429","1095-7170"]},"user_id":"15701","title":"On the Approximation of Complicated Dynamical Behavior"},{"date_updated":"2022-01-06T06:52:52Z","_id":"16572","doi":"10.1002/gamm.200910004","page":"47-60","type":"journal_article","year":"2009","citation":{"ieee":"M. Dellnitz, G. Froyland, C. Horenkamp, and K. Padberg, “On the Approximation of Transport Phenomena - a Dynamical Systems Approach,” GAMM-Mitteilungen, pp. 47–60, 2009.","short":"M. Dellnitz, G. Froyland, C. Horenkamp, K. Padberg, GAMM-Mitteilungen (2009) 47–60.","mla":"Dellnitz, Michael, et al. “On the Approximation of Transport Phenomena - a Dynamical Systems Approach.” GAMM-Mitteilungen, 2009, pp. 47–60, doi:10.1002/gamm.200910004.","bibtex":"@article{Dellnitz_Froyland_Horenkamp_Padberg_2009, title={On the Approximation of Transport Phenomena - a Dynamical Systems Approach}, DOI={10.1002/gamm.200910004}, journal={GAMM-Mitteilungen}, author={Dellnitz, Michael and Froyland, Gary and Horenkamp, Christian and Padberg, Kathrin}, year={2009}, pages={47–60} }","ama":"Dellnitz M, Froyland G, Horenkamp C, Padberg K. On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen. 2009:47-60. doi:10.1002/gamm.200910004","apa":"Dellnitz, M., Froyland, G., Horenkamp, C., & Padberg, K. (2009). On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 47–60. https://doi.org/10.1002/gamm.200910004","chicago":"Dellnitz, Michael, Gary Froyland, Christian Horenkamp, and Kathrin Padberg. “On the Approximation of Transport Phenomena - a Dynamical Systems Approach.” GAMM-Mitteilungen, 2009, 47–60. https://doi.org/10.1002/gamm.200910004."},"language":[{"iso":"eng"}],"title":"On the Approximation of Transport Phenomena - a Dynamical Systems Approach","user_id":"15701","department":[{"_id":"101"}],"publication":"GAMM-Mitteilungen","author":[{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"full_name":"Froyland, Gary","first_name":"Gary","last_name":"Froyland"},{"last_name":"Horenkamp","first_name":"Christian","full_name":"Horenkamp, Christian"},{"full_name":"Padberg, Kathrin","first_name":"Kathrin","last_name":"Padberg"}],"publication_identifier":{"issn":["0936-7195","1522-2608"]},"publication_status":"published","date_created":"2020-04-16T05:01:31Z","status":"public"},{"doi":"10.3934/jcd.2016005","date_updated":"2022-01-06T06:52:52Z","_id":"16580","page":"5-5","year":"2016","type":"journal_article","citation":{"ieee":"A. Ziessler, M. H.-V. Molo, and M. Dellnitz, “On the computation of attractors for delay differential equations,” Journal of Computational Dynamics, pp. 5–5, 2016.","short":"A. Ziessler, M.H.-V. Molo, M. Dellnitz, Journal of Computational Dynamics (2016) 5–5.","mla":"Ziessler, Adrian, et al. “On the Computation of Attractors for Delay Differential Equations.” Journal of Computational Dynamics, 2016, pp. 5–5, doi:10.3934/jcd.2016005.","bibtex":"@article{Ziessler_Molo_Dellnitz_2016, title={On the computation of attractors for delay differential equations}, DOI={10.3934/jcd.2016005}, journal={Journal of Computational Dynamics}, author={Ziessler, Adrian and Molo, Mirko Hessel-Von and Dellnitz, Michael}, year={2016}, pages={5–5} }","apa":"Ziessler, A., Molo, M. H.-V., & Dellnitz, M. (2016). On the computation of attractors for delay differential equations. Journal of Computational Dynamics, 5–5. https://doi.org/10.3934/jcd.2016005","ama":"Ziessler A, Molo MH-V, Dellnitz M. On the computation of attractors for delay differential equations. Journal of Computational Dynamics. 2016:5-5. doi:10.3934/jcd.2016005","chicago":"Ziessler, Adrian, Mirko Hessel-Von Molo, and Michael Dellnitz. “On the Computation of Attractors for Delay Differential Equations.” Journal of Computational Dynamics, 2016, 5–5. https://doi.org/10.3934/jcd.2016005."},"language":[{"iso":"eng"}],"title":"On the computation of attractors for delay differential equations","user_id":"15701","publication_identifier":{"issn":["2158-2491"]},"publication_status":"published","date_created":"2020-04-16T05:38:13Z","status":"public","department":[{"_id":"101"}],"publication":"Journal of Computational Dynamics","author":[{"last_name":"Ziessler","full_name":"Ziessler, Adrian","first_name":"Adrian"},{"last_name":"Molo","full_name":"Molo, Mirko Hessel-Von","first_name":"Mirko Hessel-Von"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"}]},{"date_updated":"2024-01-03T17:00:48Z","language":[{"iso":"eng"}],"external_id":{"arxiv":["2305.06632"]},"related_material":{"link":[{"relation":"supplementary_material","url":"https://math.uni-paderborn.de/en/ag/chair-of-applied-mathematics/research/research-projects/swarmdynamics"}]},"title":"On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies","department":[{"_id":"101"}],"project":[{"_id":"106","grant_number":"453112019","name":"Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme"}],"publication_status":"submitted","_id":"44840","main_file_link":[{"url":"https://arxiv.org/abs/2305.06632"}],"page":"38","year":"2023","type":"preprint","citation":{"ieee":"R. Gerlach, S. von der Gracht, and M. Dellnitz, “On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies,” arXiv:2305.06632. .","short":"R. Gerlach, S. von der Gracht, M. Dellnitz, ArXiv:2305.06632 (n.d.).","mla":"Gerlach, Raphael, et al. “On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies.” ArXiv:2305.06632.","bibtex":"@article{Gerlach_von der Gracht_Dellnitz, title={On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies}, journal={arXiv:2305.06632}, author={Gerlach, Raphael and von der Gracht, Sören and Dellnitz, Michael} }","chicago":"Gerlach, Raphael, Sören von der Gracht, and Michael Dellnitz. “On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies.” ArXiv:2305.06632, n.d.","apa":"Gerlach, R., von der Gracht, S., & Dellnitz, M. (n.d.). On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies. In arXiv:2305.06632.","ama":"Gerlach R, von der Gracht S, Dellnitz M. On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies. arXiv:230506632."},"abstract":[{"lang":"eng","text":"In this article we investigate the convergence behavior of gathering protocols with fixed circulant topologies using tools form dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we model a gathering protocol as a system of ordinary differential equations whose equilibria are exactly all possible gathering points. Then, we find necessary and sufficient conditions for the structure of the underlying interaction graph such that the protocol is stable and converging, i.e., gathering, in the distributive computing sense by using tools from dynamical systems. Moreover, these tools allow for a more fine grained analysis in terms of speed of convergence in the dynamical systems sense. In fact, we derive a decomposition\r\nof the state space into stable invariant subspaces with different convergence\r\nrates. In particular, this decomposition is identical for every (linear)\r\ncirculant gathering protocol, whereas only the convergence rates depend on the\r\nweights in interaction graph itself."}],"user_id":"32655","publication":"arXiv:2305.06632","keyword":["Dynamical Systems","Coupled Systems","Distributed Computing","Robot Swarms","Autonomous Mobile Robots","Gathering"],"author":[{"first_name":"Raphael","full_name":"Gerlach, Raphael","last_name":"Gerlach","id":"32655"},{"id":"97359","last_name":"von der Gracht","full_name":"von der Gracht, Sören","orcid":"0000-0002-8054-2058","first_name":"Sören"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"}],"date_created":"2023-05-12T10:16:06Z","status":"public"},{"issue":"2","intvolume":" 35","_id":"16712","type":"journal_article","year":"2020","citation":{"apa":"Dellnitz, M., Gebken, B., Gerlach, R., & Klus, S. (2020). On the equivariance properties of self-adjoint matrices. Dynamical Systems, 35(2), 197–215. https://doi.org/10.1080/14689367.2019.1661355","ama":"Dellnitz M, Gebken B, Gerlach R, Klus S. On the equivariance properties of self-adjoint matrices. Dynamical Systems. 2020;35(2):197-215. doi:10.1080/14689367.2019.1661355","chicago":"Dellnitz, Michael, Bennet Gebken, Raphael Gerlach, and Stefan Klus. “On the Equivariance Properties of Self-Adjoint Matrices.” Dynamical Systems 35, no. 2 (2020): 197–215. https://doi.org/10.1080/14689367.2019.1661355.","mla":"Dellnitz, Michael, et al. “On the Equivariance Properties of Self-Adjoint Matrices.” Dynamical Systems, vol. 35, no. 2, 2020, pp. 197–215, doi:10.1080/14689367.2019.1661355.","bibtex":"@article{Dellnitz_Gebken_Gerlach_Klus_2020, title={On the equivariance properties of self-adjoint matrices}, volume={35}, DOI={10.1080/14689367.2019.1661355}, number={2}, journal={Dynamical Systems}, author={Dellnitz, Michael and Gebken, Bennet and Gerlach, Raphael and Klus, Stefan}, year={2020}, pages={197–215} }","short":"M. Dellnitz, B. Gebken, R. Gerlach, S. Klus, Dynamical Systems 35 (2020) 197–215.","ieee":"M. Dellnitz, B. Gebken, R. Gerlach, and S. Klus, “On the equivariance properties of self-adjoint matrices,” Dynamical Systems, vol. 35, no. 2, pp. 197–215, 2020, doi: 10.1080/14689367.2019.1661355."},"page":"197-215","main_file_link":[{"url":"https://doi.org/10.1080/14689367.2019.1661355"}],"user_id":"32655","abstract":[{"lang":"eng","text":"We investigate self-adjoint matrices A∈Rn,n with respect to their equivariance properties. We show in particular that a matrix is self-adjoint if and only if it is equivariant with respect to the action of a group Γ2(A)⊂O(n) which is isomorphic to ⊗nk=1Z2. If the self-adjoint matrix possesses multiple eigenvalues – this may, for instance, be induced by symmetry properties of an underlying dynamical system – then A is even equivariant with respect to the action of a group Γ(A)≃∏ki=1O(mi) where m1,…,mk are the multiplicities of the eigenvalues λ1,…,λk of A. We discuss implications of this result for equivariant bifurcation problems, and we briefly address further applications for the Procrustes problem, graph symmetries and Taylor expansions."}],"volume":35,"status":"public","date_created":"2020-04-16T14:07:25Z","author":[{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"},{"full_name":"Gebken, Bennet","first_name":"Bennet","id":"32643","last_name":"Gebken"},{"first_name":"Raphael","full_name":"Gerlach, Raphael","last_name":"Gerlach","id":"32655"},{"last_name":"Klus","first_name":"Stefan","full_name":"Klus, Stefan"}],"publication":"Dynamical Systems","doi":"10.1080/14689367.2019.1661355","date_updated":"2023-11-17T13:12:59Z","language":[{"iso":"eng"}],"title":"On the equivariance properties of self-adjoint matrices","publication_status":"published","publication_identifier":{"issn":["1468-9367","1468-9375"]},"department":[{"_id":"101"}]},{"publication":"Journal of Global Optimization","author":[{"last_name":"Gebken","id":"32643","first_name":"Bennet","full_name":"Gebken, Bennet"},{"orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian","id":"47427","last_name":"Peitz"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"date_created":"2019-07-10T08:13:31Z","status":"public","volume":73,"abstract":[{"text":"In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems where only a subset of the set of objective functions is taken into account. If the Pareto critical set is completely described by its boundary (e.g., if we have more objective functions than dimensions in decision space), then this can be used to efficiently solve the MOP by solving a number of MOPs with fewer objective functions. If this is not the case, the results can still give insight into the structure of the Pareto critical set.","lang":"eng"}],"article_type":"original","user_id":"47427","page":"891-913","type":"journal_article","year":"2019","citation":{"ieee":"B. Gebken, S. Peitz, and M. Dellnitz, “On the hierarchical structure of Pareto critical sets,” Journal of Global Optimization, vol. 73, no. 4, pp. 891–913, 2019.","short":"B. Gebken, S. Peitz, M. Dellnitz, Journal of Global Optimization 73 (2019) 891–913.","bibtex":"@article{Gebken_Peitz_Dellnitz_2019, title={On the hierarchical structure of Pareto critical sets}, volume={73}, DOI={10.1007/s10898-019-00737-6}, number={4}, journal={Journal of Global Optimization}, author={Gebken, Bennet and Peitz, Sebastian and Dellnitz, Michael}, year={2019}, pages={891–913} }","mla":"Gebken, Bennet, et al. “On the Hierarchical Structure of Pareto Critical Sets.” Journal of Global Optimization, vol. 73, no. 4, 2019, pp. 891–913, doi:10.1007/s10898-019-00737-6.","apa":"Gebken, B., Peitz, S., & Dellnitz, M. (2019). On the hierarchical structure of Pareto critical sets. Journal of Global Optimization, 73(4), 891–913. https://doi.org/10.1007/s10898-019-00737-6","ama":"Gebken B, Peitz S, Dellnitz M. On the hierarchical structure of Pareto critical sets. Journal of Global Optimization. 2019;73(4):891-913. doi:10.1007/s10898-019-00737-6","chicago":"Gebken, Bennet, Sebastian Peitz, and Michael Dellnitz. “On the Hierarchical Structure of Pareto Critical Sets.” Journal of Global Optimization 73, no. 4 (2019): 891–913. https://doi.org/10.1007/s10898-019-00737-6."},"_id":"10595","intvolume":" 73","issue":"4","department":[{"_id":"101"}],"publication_identifier":{"issn":["0925-5001","1573-2916"]},"publication_status":"published","title":"On the hierarchical structure of Pareto critical sets","language":[{"iso":"eng"}],"date_updated":"2022-01-06T06:50:46Z","doi":"10.1007/s10898-019-00737-6"},{"user_id":"15701","title":"On the isolated spectrum of the Perron-Frobenius operator","publication":"Nonlinearity","department":[{"_id":"101"}],"author":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"full_name":"Froyland, Gary","first_name":"Gary","last_name":"Froyland"},{"full_name":"Sertl, Stefan","first_name":"Stefan","last_name":"Sertl"}],"date_created":"2020-04-15T09:09:46Z","status":"public","publication_status":"published","publication_identifier":{"issn":["0951-7715","1361-6544"]},"_id":"16554","date_updated":"2022-01-06T06:52:52Z","doi":"10.1088/0951-7715/13/4/310","language":[{"iso":"eng"}],"page":"1171-1188","year":"2000","type":"journal_article","citation":{"short":"M. Dellnitz, G. Froyland, S. Sertl, Nonlinearity (2000) 1171–1188.","ieee":"M. Dellnitz, G. Froyland, and S. Sertl, “On the isolated spectrum of the Perron-Frobenius operator,” Nonlinearity, pp. 1171–1188, 2000.","chicago":"Dellnitz, Michael, Gary Froyland, and Stefan Sertl. “On the Isolated Spectrum of the Perron-Frobenius Operator.” Nonlinearity, 2000, 1171–88. https://doi.org/10.1088/0951-7715/13/4/310.","apa":"Dellnitz, M., Froyland, G., & Sertl, S. (2000). On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 1171–1188. https://doi.org/10.1088/0951-7715/13/4/310","ama":"Dellnitz M, Froyland G, Sertl S. On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity. 2000:1171-1188. doi:10.1088/0951-7715/13/4/310","bibtex":"@article{Dellnitz_Froyland_Sertl_2000, title={On the isolated spectrum of the Perron-Frobenius operator}, DOI={10.1088/0951-7715/13/4/310}, journal={Nonlinearity}, author={Dellnitz, Michael and Froyland, Gary and Sertl, Stefan}, year={2000}, pages={1171–1188} }","mla":"Dellnitz, Michael, et al. “On the Isolated Spectrum of the Perron-Frobenius Operator.” Nonlinearity, 2000, pp. 1171–88, doi:10.1088/0951-7715/13/4/310."}},{"author":[{"last_name":"Gail","full_name":"Gail, Tobias","first_name":"Tobias"},{"last_name":"Leyendecker","first_name":"Sigrid","full_name":"Leyendecker, Sigrid"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"}],"publication":"The 3rdJoint International Conference on Multibody System Dynamics","department":[{"_id":"101"}],"status":"public","date_created":"2020-05-20T08:32:33Z","title":"On the role of quadrature rules and system dimensions in variational multirateintegrators","user_id":"47427","citation":{"chicago":"Gail, Tobias, Sigrid Leyendecker, and Sina Ober-Blöbaum. “On the Role of Quadrature Rules and System Dimensions in Variational Multirateintegrators.” In The 3rdJoint International Conference on Multibody System Dynamics, 2014.","ama":"Gail T, Leyendecker S, Ober-Blöbaum S. On the role of quadrature rules and system dimensions in variational multirateintegrators. In: The 3rdJoint International Conference on Multibody System Dynamics. ; 2014.","apa":"Gail, T., Leyendecker, S., & Ober-Blöbaum, S. (2014). On the role of quadrature rules and system dimensions in variational multirateintegrators. In The 3rdJoint International Conference on Multibody System Dynamics.","mla":"Gail, Tobias, et al. “On the Role of Quadrature Rules and System Dimensions in Variational Multirateintegrators.” The 3rdJoint International Conference on Multibody System Dynamics, 2014.","bibtex":"@inproceedings{Gail_Leyendecker_Ober-Blöbaum_2014, title={On the role of quadrature rules and system dimensions in variational multirateintegrators}, booktitle={The 3rdJoint International Conference on Multibody System Dynamics}, author={Gail, Tobias and Leyendecker, Sigrid and Ober-Blöbaum, Sina}, year={2014} }","short":"T. Gail, S. Leyendecker, S. Ober-Blöbaum, in: The 3rdJoint International Conference on Multibody System Dynamics, 2014.","ieee":"T. Gail, S. Leyendecker, and S. Ober-Blöbaum, “On the role of quadrature rules and system dimensions in variational multirateintegrators,” in The 3rdJoint International Conference on Multibody System Dynamics, 2014."},"year":"2014","type":"conference","language":[{"iso":"eng"}],"_id":"17045","date_updated":"2022-01-06T06:53:03Z"},{"date_updated":"2023-03-11T17:16:33Z","oa":"1","doi":"10.1007/s10898-022-01223-2","language":[{"iso":"eng"}],"title":"On the structure of regularization paths for piecewise differentiable regularization terms","department":[{"_id":"101"},{"_id":"655"}],"intvolume":" 85","_id":"27426","issue":"3","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01223-2.pdf"}],"type":"journal_article","citation":{"ieee":"B. Gebken, K. Bieker, and S. Peitz, “On the structure of regularization paths for piecewise differentiable regularization terms,” Journal of Global Optimization, vol. 85, no. 3, pp. 709–741, 2023, doi: 10.1007/s10898-022-01223-2.","short":"B. Gebken, K. Bieker, S. Peitz, Journal of Global Optimization 85 (2023) 709–741.","mla":"Gebken, Bennet, et al. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” Journal of Global Optimization, vol. 85, no. 3, 2023, pp. 709–41, doi:10.1007/s10898-022-01223-2.","bibtex":"@article{Gebken_Bieker_Peitz_2023, title={On the structure of regularization paths for piecewise differentiable regularization terms}, volume={85}, DOI={10.1007/s10898-022-01223-2}, number={3}, journal={Journal of Global Optimization}, author={Gebken, Bennet and Bieker, Katharina and Peitz, Sebastian}, year={2023}, pages={709–741} }","apa":"Gebken, B., Bieker, K., & Peitz, S. (2023). On the structure of regularization paths for piecewise differentiable regularization terms. Journal of Global Optimization, 85(3), 709–741. https://doi.org/10.1007/s10898-022-01223-2","ama":"Gebken B, Bieker K, Peitz S. On the structure of regularization paths for piecewise differentiable regularization terms. Journal of Global Optimization. 2023;85(3):709-741. doi:10.1007/s10898-022-01223-2","chicago":"Gebken, Bennet, Katharina Bieker, and Sebastian Peitz. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” Journal of Global Optimization 85, no. 3 (2023): 709–41. https://doi.org/10.1007/s10898-022-01223-2."},"year":"2023","page":"709-741","abstract":[{"lang":"eng","text":"Regularization is used in many different areas of optimization when solutions\r\nare sought which not only minimize a given function, but also possess a certain\r\ndegree of regularity. Popular applications are image denoising, sparse\r\nregression and machine learning. Since the choice of the regularization\r\nparameter is crucial but often difficult, path-following methods are used to\r\napproximate the entire regularization path, i.e., the set of all possible\r\nsolutions for all regularization parameters. Due to their nature, the\r\ndevelopment of these methods requires structural results about the\r\nregularization path. The goal of this article is to derive these results for\r\nthe case of a smooth objective function which is penalized by a piecewise\r\ndifferentiable regularization term. We do this by treating regularization as a\r\nmultiobjective optimization problem. Our results suggest that even in this\r\ngeneral case, the regularization path is piecewise smooth. Moreover, our theory\r\nallows for a classification of the nonsmooth features that occur in between\r\nsmooth parts. This is demonstrated in two applications, namely support-vector\r\nmachines and exact penalty methods."}],"user_id":"47427","author":[{"first_name":"Bennet","full_name":"Gebken, Bennet","last_name":"Gebken","id":"32643"},{"id":"32829","last_name":"Bieker","full_name":"Bieker, Katharina","first_name":"Katharina"},{"last_name":"Peitz","id":"47427","first_name":"Sebastian","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian"}],"publication":"Journal of Global Optimization","status":"public","date_created":"2021-11-15T09:24:59Z","volume":85},{"language":[{"iso":"eng"}],"date_updated":"2022-10-21T12:27:16Z","oa":"1","doi":"10.1109/TPAMI.2021.3114962","department":[{"_id":"101"},{"_id":"530"},{"_id":"655"}],"publication_status":"epub_ahead","title":"On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation","main_file_link":[{"url":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9547772","open_access":"1"}],"page":"7797-7808","type":"journal_article","citation":{"mla":"Bieker, Katharina, et al. “On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation.” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 44, no. 11, IEEE, 2022, pp. 7797–808, doi:10.1109/TPAMI.2021.3114962.","bibtex":"@article{Bieker_Gebken_Peitz_2022, title={On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation}, volume={44}, DOI={10.1109/TPAMI.2021.3114962}, number={11}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, publisher={IEEE}, author={Bieker, Katharina and Gebken, Bennet and Peitz, Sebastian}, year={2022}, pages={7797–7808} }","apa":"Bieker, K., Gebken, B., & Peitz, S. (2022). On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(11), 7797–7808. https://doi.org/10.1109/TPAMI.2021.3114962","ama":"Bieker K, Gebken B, Peitz S. On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2022;44(11):7797-7808. doi:10.1109/TPAMI.2021.3114962","chicago":"Bieker, Katharina, Bennet Gebken, and Sebastian Peitz. “On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation.” IEEE Transactions on Pattern Analysis and Machine Intelligence 44, no. 11 (2022): 7797–7808. https://doi.org/10.1109/TPAMI.2021.3114962.","ieee":"K. Bieker, B. Gebken, and S. Peitz, “On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 44, no. 11, pp. 7797–7808, 2022, doi: 10.1109/TPAMI.2021.3114962.","short":"K. Bieker, B. Gebken, S. Peitz, IEEE Transactions on Pattern Analysis and Machine Intelligence 44 (2022) 7797–7808."},"year":"2022","_id":"20731","intvolume":" 44","issue":"11","file":[{"date_created":"2021-09-25T11:59:15Z","file_name":"On_the_Treatment_of_Optimization_Problems_with_L1_Penalty_Terms_via_Multiobjective_Continuation.pdf","access_level":"closed","creator":"speitz","file_id":"25040","file_size":7990831,"success":1,"relation":"main_file","content_type":"application/pdf","date_updated":"2021-09-25T11:59:15Z"}],"file_date_updated":"2021-09-25T11:59:15Z","publication":"IEEE Transactions on Pattern Analysis and Machine Intelligence","publisher":"IEEE","author":[{"id":"32829","last_name":"Bieker","full_name":"Bieker, Katharina","first_name":"Katharina"},{"last_name":"Gebken","id":"32643","first_name":"Bennet","full_name":"Gebken, Bennet"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427"}],"date_created":"2020-12-15T07:46:36Z","has_accepted_license":"1","status":"public","volume":44,"abstract":[{"text":"We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scientific areas such as image and signal processing, medical imaging, compressed sensing, and machine learning (e.g., for the training of neural networks). Sparsity is an important feature to ensure robustness against noisy data, but also to find models that are interpretable and easy to analyze due to the small number of relevant terms. It is common practice to enforce sparsity by adding the ℓ1-norm as a weighted penalty term. In order to gain a better understanding and to allow for an informed model selection, we directly solve the corresponding multiobjective optimization problem (MOP) that arises when we minimize the main objective and the ℓ1-norm simultaneously. As this MOP is in general non-convex for nonlinear objectives, the weighting method will fail to provide all optimal compromises. To avoid this issue, we present a continuation method which is specifically tailored to MOPs with two objective functions one of which is the ℓ1-norm. Our method can be seen as a generalization of well-known homotopy methods for linear regression problems to the nonlinear case. Several numerical examples - including neural network training - demonstrate our theoretical findings and the additional insight that can be gained by this multiobjective approach.","lang":"eng"}],"article_type":"original","user_id":"47427","ddc":["510"]},{"abstract":[{"lang":"eng","text":"As in almost every other branch of science, the major advances in data\r\nscience and machine learning have also resulted in significant improvements\r\nregarding the modeling and simulation of nonlinear dynamical systems. It is\r\nnowadays possible to make accurate medium to long-term predictions of highly\r\ncomplex systems such as the weather, the dynamics within a nuclear fusion\r\nreactor, of disease models or the stock market in a very efficient manner. In\r\nmany cases, predictive methods are advertised to ultimately be useful for\r\ncontrol, as the control of high-dimensional nonlinear systems is an engineering\r\ngrand challenge with huge potential in areas such as clean and efficient energy\r\nproduction, or the development of advanced medical devices. However, the\r\nquestion of how to use a predictive model for control is often left unanswered\r\ndue to the associated challenges, namely a significantly higher system\r\ncomplexity, the requirement of much larger data sets and an increased and often\r\nproblem-specific modeling effort. To solve these issues, we present a universal\r\nframework (which we call QuaSiModO:\r\nQuantization-Simulation-Modeling-Optimization) to transform arbitrary\r\npredictive models into control systems and use them for feedback control. The\r\nadvantages of our approach are a linear increase in data requirements with\r\nrespect to the control dimension, performance guarantees that rely exclusively\r\non the accuracy of the predictive model, and only little prior knowledge\r\nrequirements in control theory to solve complex control problems. In particular\r\nthe latter point is of key importance to enable a large number of researchers\r\nand practitioners to exploit the ever increasing capabilities of predictive\r\nmodels for control in a straight-forward and systematic fashion."}],"user_id":"47427","publisher":"Elsevier","author":[{"id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian"},{"id":"32829","last_name":"Bieker","full_name":"Bieker, Katharina","first_name":"Katharina"}],"publication":"Automatica","status":"public","date_created":"2021-02-10T07:04:15Z","volume":149,"_id":"21199","intvolume":" 149","article_number":"110840","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0005109822007075/pdfft?isDTMRedir=true&download=true","open_access":"1"}],"citation":{"short":"S. Peitz, K. Bieker, Automatica 149 (2023).","ieee":"S. Peitz and K. Bieker, “On the Universal Transformation of Data-Driven Models to Control Systems,” Automatica, vol. 149, Art. no. 110840, 2023, doi: 10.1016/j.automatica.2022.110840.","chicago":"Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of Data-Driven Models to Control Systems.” Automatica 149 (2023). https://doi.org/10.1016/j.automatica.2022.110840.","apa":"Peitz, S., & Bieker, K. (2023). On the Universal Transformation of Data-Driven Models to Control Systems. Automatica, 149, Article 110840. https://doi.org/10.1016/j.automatica.2022.110840","ama":"Peitz S, Bieker K. On the Universal Transformation of Data-Driven Models to Control Systems. Automatica. 2023;149. doi:10.1016/j.automatica.2022.110840","bibtex":"@article{Peitz_Bieker_2023, title={On the Universal Transformation of Data-Driven Models to Control Systems}, volume={149}, DOI={10.1016/j.automatica.2022.110840}, number={110840}, journal={Automatica}, publisher={Elsevier}, author={Peitz, Sebastian and Bieker, Katharina}, year={2023} }","mla":"Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of Data-Driven Models to Control Systems.” Automatica, vol. 149, 110840, Elsevier, 2023, doi:10.1016/j.automatica.2022.110840."},"year":"2023","type":"journal_article","title":"On the Universal Transformation of Data-Driven Models to Control Systems","department":[{"_id":"101"},{"_id":"655"}],"project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"publication_status":"published","date_updated":"2023-01-07T12:01:58Z","oa":"1","doi":"10.1016/j.automatica.2022.110840","language":[{"iso":"eng"}]},{"title":"Optimal control of a switched reluctance drive by a direct method using a discrete variational principle","user_id":"15701","author":[{"last_name":"Flasskamp","full_name":"Flasskamp, Kathrin","first_name":"Kathrin"},{"first_name":"Sina","full_name":"Ober-Blobaum, Sina","last_name":"Ober-Blobaum"},{"last_name":"Schneider","first_name":"Tobias","full_name":"Schneider, Tobias"},{"last_name":"Bocker","first_name":"Joachim","full_name":"Bocker, Joachim"}],"department":[{"_id":"101"}],"publication":"52nd IEEE Conference on Decision and Control","publication_status":"published","publication_identifier":{"isbn":["9781467357173","9781467357142","9781479913817"]},"status":"public","date_created":"2020-04-16T05:59:29Z","date_updated":"2022-01-06T06:52:52Z","_id":"16596","doi":"10.1109/cdc.2013.6761075","citation":{"bibtex":"@inproceedings{Flasskamp_Ober-Blobaum_Schneider_Bocker_2014, title={Optimal control of a switched reluctance drive by a direct method using a discrete variational principle}, DOI={10.1109/cdc.2013.6761075}, booktitle={52nd IEEE Conference on Decision and Control}, author={Flasskamp, Kathrin and Ober-Blobaum, Sina and Schneider, Tobias and Bocker, Joachim}, year={2014} }","mla":"Flasskamp, Kathrin, et al. “Optimal Control of a Switched Reluctance Drive by a Direct Method Using a Discrete Variational Principle.” 52nd IEEE Conference on Decision and Control, 2014, doi:10.1109/cdc.2013.6761075.","ama":"Flasskamp K, Ober-Blobaum S, Schneider T, Bocker J. Optimal control of a switched reluctance drive by a direct method using a discrete variational principle. In: 52nd IEEE Conference on Decision and Control. ; 2014. doi:10.1109/cdc.2013.6761075","apa":"Flasskamp, K., Ober-Blobaum, S., Schneider, T., & Bocker, J. (2014). Optimal control of a switched reluctance drive by a direct method using a discrete variational principle. In 52nd IEEE Conference on Decision and Control. https://doi.org/10.1109/cdc.2013.6761075","chicago":"Flasskamp, Kathrin, Sina Ober-Blobaum, Tobias Schneider, and Joachim Bocker. “Optimal Control of a Switched Reluctance Drive by a Direct Method Using a Discrete Variational Principle.” In 52nd IEEE Conference on Decision and Control, 2014. https://doi.org/10.1109/cdc.2013.6761075.","ieee":"K. Flasskamp, S. Ober-Blobaum, T. Schneider, and J. Bocker, “Optimal control of a switched reluctance drive by a direct method using a discrete variational principle,” in 52nd IEEE Conference on Decision and Control, 2014.","short":"K. Flasskamp, S. Ober-Blobaum, T. Schneider, J. Bocker, in: 52nd IEEE Conference on Decision and Control, 2014."},"type":"conference","year":"2014"},{"doi":"10.1002/pamm.201210350","_id":"16593","date_updated":"2022-01-06T06:52:52Z","page":"723-724","year":"2012","citation":{"ama":"Flaßkamp K, Timmermann J, Ober-Blöbaum S, Dellnitz M, Trächtler A. Optimal Control on Stable Manifolds for a Double Pendulum. PAMM. 2012:723-724. doi:10.1002/pamm.201210350","apa":"Flaßkamp, K., Timmermann, J., Ober-Blöbaum, S., Dellnitz, M., & Trächtler, A. (2012). Optimal Control on Stable Manifolds for a Double Pendulum. PAMM, 723–724. https://doi.org/10.1002/pamm.201210350","chicago":"Flaßkamp, Kathrin, Julia Timmermann, Sina Ober-Blöbaum, Michael Dellnitz, and Ansgar Trächtler. “Optimal Control on Stable Manifolds for a Double Pendulum.” PAMM, 2012, 723–24. https://doi.org/10.1002/pamm.201210350.","mla":"Flaßkamp, Kathrin, et al. “Optimal Control on Stable Manifolds for a Double Pendulum.” PAMM, 2012, pp. 723–24, doi:10.1002/pamm.201210350.","bibtex":"@article{Flaßkamp_Timmermann_Ober-Blöbaum_Dellnitz_Trächtler_2012, title={Optimal Control on Stable Manifolds for a Double Pendulum}, DOI={10.1002/pamm.201210350}, journal={PAMM}, author={Flaßkamp, Kathrin and Timmermann, Julia and Ober-Blöbaum, Sina and Dellnitz, Michael and Trächtler, Ansgar}, year={2012}, pages={723–724} }","short":"K. Flaßkamp, J. Timmermann, S. Ober-Blöbaum, M. Dellnitz, A. Trächtler, PAMM (2012) 723–724.","ieee":"K. Flaßkamp, J. Timmermann, S. Ober-Blöbaum, M. Dellnitz, and A. Trächtler, “Optimal Control on Stable Manifolds for a Double Pendulum,” PAMM, pp. 723–724, 2012."},"type":"journal_article","language":[{"iso":"eng"}],"title":"Optimal Control on Stable Manifolds for a Double Pendulum","user_id":"15701","publication_status":"published","publication_identifier":{"issn":["1617-7061"]},"date_created":"2020-04-16T05:54:36Z","status":"public","publication":"PAMM","department":[{"_id":"101"}],"author":[{"first_name":"Kathrin","full_name":"Flaßkamp, Kathrin","last_name":"Flaßkamp"},{"first_name":"Julia","full_name":"Timmermann, Julia","last_name":"Timmermann"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"},{"last_name":"Trächtler","first_name":"Ansgar","full_name":"Trächtler, Ansgar"}]},{"language":[{"iso":"eng"}],"type":"journal_article","citation":{"apa":"Elsässer, R., Monien, B., Preis, R., & Frommer, A. (2004). Optimal Diffusion Schemes and Load Balancing on Product Graphs. Parallel Processing Letters, 61–73. https://doi.org/10.1142/s0129626404001714","ama":"Elsässer R, Monien B, Preis R, Frommer A. Optimal Diffusion Schemes and Load Balancing on Product Graphs. Parallel Processing Letters. 2004:61-73. doi:10.1142/s0129626404001714","chicago":"Elsässer, Robert, Burkhard Monien, Robert Preis, and Andreas Frommer. “Optimal Diffusion Schemes and Load Balancing on Product Graphs.” Parallel Processing Letters, 2004, 61–73. https://doi.org/10.1142/s0129626404001714.","mla":"Elsässer, Robert, et al. “Optimal Diffusion Schemes and Load Balancing on Product Graphs.” Parallel Processing Letters, 2004, pp. 61–73, doi:10.1142/s0129626404001714.","bibtex":"@article{Elsässer_Monien_Preis_Frommer_2004, title={Optimal Diffusion Schemes and Load Balancing on Product Graphs}, DOI={10.1142/s0129626404001714}, journal={Parallel Processing Letters}, author={Elsässer, Robert and Monien, Burkhard and Preis, Robert and Frommer, Andreas}, year={2004}, pages={61–73} }","short":"R. Elsässer, B. Monien, R. Preis, A. Frommer, Parallel Processing Letters (2004) 61–73.","ieee":"R. Elsässer, B. Monien, R. Preis, and A. Frommer, “Optimal Diffusion Schemes and Load Balancing on Product Graphs,” Parallel Processing Letters, pp. 61–73, 2004."},"year":"2004","page":"61-73","date_updated":"2022-01-06T06:52:52Z","_id":"16587","doi":"10.1142/s0129626404001714","author":[{"full_name":"Elsässer, Robert","first_name":"Robert","last_name":"Elsässer"},{"last_name":"Monien","full_name":"Monien, Burkhard","first_name":"Burkhard"},{"first_name":"Robert","full_name":"Preis, Robert","last_name":"Preis"},{"last_name":"Frommer","full_name":"Frommer, Andreas","first_name":"Andreas"}],"department":[{"_id":"101"}],"publication":"Parallel Processing Letters","status":"public","date_created":"2020-04-16T05:46:56Z","publication_status":"published","publication_identifier":{"issn":["0129-6264","1793-642X"]},"abstract":[{"lang":"eng","text":" We discuss nearest neighbor load balancing schemes on processor networks which are represented by a cartesian product of graphs and present a new optimal diffusion scheme for general graphs. In the first part of the paper, we introduce the Alternating-Direction load balancing scheme, which reduces the number of load balance iterations by a factor of 2 for cartesian products of graphs. The resulting flow is theoretically analyzed and can be very high for certain cases. Therefore, we further present the Mixed-Direction scheme which needs the same number of iterations but computes in most cases a much smaller flow. In the second part of the paper, we present a simple optimal diffusion scheme for general graphs, calculating a balancing flow which is minimal in the l2 norm. It is based on the spectra of the graph representing the network and needs only m-1 iterations to balance the load with m being the number of distinct eigenvalues. Known optimal diffusion schemes have the same performance, however the optimal scheme presented in this paper can be implemented in a very simple manner. The number of iterations of optimal diffusion schemes is independent of the load scenario and, thus, they are practical for networks which represent graphs with known spectra. Finally, our experiments exhibit that the new optimal scheme can successfully be combined with the Alternating-Direction and Mixed-Direction schemes for efficient load balancing on product graphs. "}],"user_id":"15701","title":"Optimal Diffusion Schemes and Load Balancing on Product Graphs"},{"date_updated":"2022-01-06T06:52:54Z","_id":"16661","doi":"10.1109/ecce.2009.5316428","year":"2009","citation":{"chicago":"Romaus, C., J. Bocker, K. Witting, A. Seifried, and O. Znamenshchykov. “Optimal Energy Management for a Hybrid Energy Storage System Combining Batteries and Double Layer Capacitors.” In 2009 IEEE Energy Conversion Congress and Exposition, 2009. https://doi.org/10.1109/ecce.2009.5316428.","apa":"Romaus, C., Bocker, J., Witting, K., Seifried, A., & Znamenshchykov, O. (2009). Optimal energy management for a hybrid energy storage system combining batteries and double layer capacitors. In 2009 IEEE Energy Conversion Congress and Exposition. https://doi.org/10.1109/ecce.2009.5316428","ama":"Romaus C, Bocker J, Witting K, Seifried A, Znamenshchykov O. Optimal energy management for a hybrid energy storage system combining batteries and double layer capacitors. In: 2009 IEEE Energy Conversion Congress and Exposition. ; 2009. doi:10.1109/ecce.2009.5316428","bibtex":"@inproceedings{Romaus_Bocker_Witting_Seifried_Znamenshchykov_2009, title={Optimal energy management for a hybrid energy storage system combining batteries and double layer capacitors}, DOI={10.1109/ecce.2009.5316428}, booktitle={2009 IEEE Energy Conversion Congress and Exposition}, author={Romaus, C. and Bocker, J. and Witting, K. and Seifried, A. and Znamenshchykov, O.}, year={2009} }","mla":"Romaus, C., et al. “Optimal Energy Management for a Hybrid Energy Storage System Combining Batteries and Double Layer Capacitors.” 2009 IEEE Energy Conversion Congress and Exposition, 2009, doi:10.1109/ecce.2009.5316428.","short":"C. Romaus, J. Bocker, K. Witting, A. Seifried, O. Znamenshchykov, in: 2009 IEEE Energy Conversion Congress and Exposition, 2009.","ieee":"C. Romaus, J. Bocker, K. Witting, A. Seifried, and O. Znamenshchykov, “Optimal energy management for a hybrid energy storage system combining batteries and double layer capacitors,” in 2009 IEEE Energy Conversion Congress and Exposition, 2009."},"type":"conference","user_id":"15701","title":"Optimal energy management for a hybrid energy storage system combining batteries and double layer capacitors","author":[{"first_name":"C.","full_name":"Romaus, C.","last_name":"Romaus"},{"full_name":"Bocker, J.","first_name":"J.","last_name":"Bocker"},{"last_name":"Witting","first_name":"K.","full_name":"Witting, K."},{"first_name":"A.","full_name":"Seifried, A.","last_name":"Seifried"},{"full_name":"Znamenshchykov, O.","first_name":"O.","last_name":"Znamenshchykov"}],"publication":"2009 IEEE Energy Conversion Congress and Exposition","department":[{"_id":"101"}],"status":"public","date_created":"2020-04-16T09:53:32Z","publication_status":"published","publication_identifier":{"isbn":["9781424428939"]}},{"type":"conference","citation":{"ieee":"O. Junge and S. Ober-Blobaum, “Optimal Reconfiguration of Formation Flying Satellites,” in Proceedings of the 44th IEEE Conference on Decision and Control, 2006.","short":"O. Junge, S. Ober-Blobaum, in: Proceedings of the 44th IEEE Conference on Decision and Control, 2006.","mla":"Junge, O., and S. Ober-Blobaum. “Optimal Reconfiguration of Formation Flying Satellites.” Proceedings of the 44th IEEE Conference on Decision and Control, 2006, doi:10.1109/cdc.2005.1582132.","bibtex":"@inproceedings{Junge_Ober-Blobaum_2006, title={Optimal Reconfiguration of Formation Flying Satellites}, DOI={10.1109/cdc.2005.1582132}, booktitle={Proceedings of the 44th IEEE Conference on Decision and Control}, author={Junge, O. and Ober-Blobaum, S.}, year={2006} }","apa":"Junge, O., & Ober-Blobaum, S. (2006). Optimal Reconfiguration of Formation Flying Satellites. In Proceedings of the 44th IEEE Conference on Decision and Control. https://doi.org/10.1109/cdc.2005.1582132","ama":"Junge O, Ober-Blobaum S. Optimal Reconfiguration of Formation Flying Satellites. In: Proceedings of the 44th IEEE Conference on Decision and Control. ; 2006. doi:10.1109/cdc.2005.1582132","chicago":"Junge, O., and S. Ober-Blobaum. “Optimal Reconfiguration of Formation Flying Satellites.” In Proceedings of the 44th IEEE Conference on Decision and Control, 2006. https://doi.org/10.1109/cdc.2005.1582132."},"year":"2006","doi":"10.1109/cdc.2005.1582132","_id":"16618","date_updated":"2022-01-06T06:52:53Z","date_created":"2020-04-16T08:10:25Z","status":"public","publication_status":"published","publication_identifier":{"isbn":["0780395670"]},"publication":"Proceedings of the 44th IEEE Conference on Decision and Control","department":[{"_id":"101"}],"author":[{"first_name":"O.","full_name":"Junge, O.","last_name":"Junge"},{"last_name":"Ober-Blobaum","full_name":"Ober-Blobaum, S.","first_name":"S."}],"user_id":"15701","title":"Optimal Reconfiguration of Formation Flying Satellites"},{"doi":"10.1109/cdc.2006.376977","date_updated":"2022-01-06T06:52:53Z","_id":"16621","citation":{"ieee":"O. Junge, J. E. Marsden, and S. Ober-Blobaum, “Optimal Reconfiguration of Formation Flying Spacecraft ---a Decentralized Approach,” in Proceedings of the 45th IEEE Conference on Decision and Control, 2006.","short":"O. Junge, J.E. Marsden, S. Ober-Blobaum, in: Proceedings of the 45th IEEE Conference on Decision and Control, 2006.","mla":"Junge, O., et al. “Optimal Reconfiguration of Formation Flying Spacecraft ---a Decentralized Approach.” Proceedings of the 45th IEEE Conference on Decision and Control, 2006, doi:10.1109/cdc.2006.376977.","bibtex":"@inproceedings{Junge_Marsden_Ober-Blobaum_2006, title={Optimal Reconfiguration of Formation Flying Spacecraft ---a Decentralized Approach}, DOI={10.1109/cdc.2006.376977}, booktitle={Proceedings of the 45th IEEE Conference on Decision and Control}, author={Junge, O. and Marsden, J.E. and Ober-Blobaum, S.}, year={2006} }","chicago":"Junge, O., J.E. Marsden, and S. Ober-Blobaum. “Optimal Reconfiguration of Formation Flying Spacecraft ---a Decentralized Approach.” In Proceedings of the 45th IEEE Conference on Decision and Control, 2006. https://doi.org/10.1109/cdc.2006.376977.","ama":"Junge O, Marsden JE, Ober-Blobaum S. Optimal Reconfiguration of Formation Flying Spacecraft ---a Decentralized Approach. In: Proceedings of the 45th IEEE Conference on Decision and Control. ; 2006. doi:10.1109/cdc.2006.376977","apa":"Junge, O., Marsden, J. E., & Ober-Blobaum, S. (2006). Optimal Reconfiguration of Formation Flying Spacecraft ---a Decentralized Approach. In Proceedings of the 45th IEEE Conference on Decision and Control. https://doi.org/10.1109/cdc.2006.376977"},"type":"conference","year":"2006","language":[{"iso":"eng"}],"title":"Optimal Reconfiguration of Formation Flying Spacecraft ---a Decentralized Approach","user_id":"15701","publication_status":"published","publication_identifier":{"isbn":["1424401712"]},"date_created":"2020-04-16T08:13:39Z","status":"public","department":[{"_id":"101"}],"publication":"Proceedings of the 45th IEEE Conference on Decision and Control","author":[{"first_name":"O.","full_name":"Junge, O.","last_name":"Junge"},{"last_name":"Marsden","full_name":"Marsden, J.E.","first_name":"J.E."},{"last_name":"Ober-Blobaum","full_name":"Ober-Blobaum, S.","first_name":"S."}]},{"doi":"10.1002/pamm.201310196","date_updated":"2022-01-06T06:52:52Z","_id":"16595","page":"401-402","type":"journal_article","year":"2013","citation":{"chicago":"Flaßkamp, Kathrin, Todd Murphey, and Sina Ober-Blöbaum. “Optimization for Discretized Switched Systems.” PAMM, 2013, 401–2. https://doi.org/10.1002/pamm.201310196.","apa":"Flaßkamp, K., Murphey, T., & Ober-Blöbaum, S. (2013). Optimization for discretized switched systems. PAMM, 401–402. https://doi.org/10.1002/pamm.201310196","ama":"Flaßkamp K, Murphey T, Ober-Blöbaum S. Optimization for discretized switched systems. PAMM. 2013:401-402. doi:10.1002/pamm.201310196","mla":"Flaßkamp, Kathrin, et al. “Optimization for Discretized Switched Systems.” PAMM, 2013, pp. 401–02, doi:10.1002/pamm.201310196.","bibtex":"@article{Flaßkamp_Murphey_Ober-Blöbaum_2013, title={Optimization for discretized switched systems}, DOI={10.1002/pamm.201310196}, journal={PAMM}, author={Flaßkamp, Kathrin and Murphey, Todd and Ober-Blöbaum, Sina}, year={2013}, pages={401–402} }","short":"K. Flaßkamp, T. Murphey, S. Ober-Blöbaum, PAMM (2013) 401–402.","ieee":"K. Flaßkamp, T. Murphey, and S. Ober-Blöbaum, “Optimization for discretized switched systems,” PAMM, pp. 401–402, 2013."},"language":[{"iso":"eng"}],"title":"Optimization for discretized switched systems","user_id":"15701","publication_status":"published","publication_identifier":{"issn":["1617-7061"]},"date_created":"2020-04-16T05:57:12Z","status":"public","department":[{"_id":"101"}],"publication":"PAMM","author":[{"first_name":"Kathrin","full_name":"Flaßkamp, Kathrin","last_name":"Flaßkamp"},{"first_name":"Todd","full_name":"Murphey, Todd","last_name":"Murphey"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"}]},{"doi":"10.3182/20110828-6-it-1002.02487","date_updated":"2022-01-06T06:52:53Z","_id":"16629","language":[{"iso":"eng"}],"page":"12611-12619","year":"2011","type":"journal_article","citation":{"chicago":"Krüger, Martin, Katrin Witting, Ansgar Trächtler, and Michael Dellnitz. “Parametric Model-Order Reduction in Hierarchical Multiobjective Optimization of Mechatronic Systems*.” IFAC Proceedings Volumes, 2011, 12611–19. https://doi.org/10.3182/20110828-6-it-1002.02487.","ama":"Krüger M, Witting K, Trächtler A, Dellnitz M. Parametric Model-Order Reduction in Hierarchical Multiobjective Optimization of Mechatronic Systems*. IFAC Proceedings Volumes. 2011:12611-12619. doi:10.3182/20110828-6-it-1002.02487","apa":"Krüger, M., Witting, K., Trächtler, A., & Dellnitz, M. (2011). Parametric Model-Order Reduction in Hierarchical Multiobjective Optimization of Mechatronic Systems*. IFAC Proceedings Volumes, 12611–12619. https://doi.org/10.3182/20110828-6-it-1002.02487","mla":"Krüger, Martin, et al. “Parametric Model-Order Reduction in Hierarchical Multiobjective Optimization of Mechatronic Systems*.” IFAC Proceedings Volumes, 2011, pp. 12611–19, doi:10.3182/20110828-6-it-1002.02487.","bibtex":"@article{Krüger_Witting_Trächtler_Dellnitz_2011, title={Parametric Model-Order Reduction in Hierarchical Multiobjective Optimization of Mechatronic Systems*}, DOI={10.3182/20110828-6-it-1002.02487}, journal={IFAC Proceedings Volumes}, author={Krüger, Martin and Witting, Katrin and Trächtler, Ansgar and Dellnitz, Michael}, year={2011}, pages={12611–12619} }","short":"M. Krüger, K. Witting, A. Trächtler, M. Dellnitz, IFAC Proceedings Volumes (2011) 12611–12619.","ieee":"M. Krüger, K. Witting, A. Trächtler, and M. Dellnitz, “Parametric Model-Order Reduction in Hierarchical Multiobjective Optimization of Mechatronic Systems*,” IFAC Proceedings Volumes, pp. 12611–12619, 2011."},"user_id":"15701","title":"Parametric Model-Order Reduction in Hierarchical Multiobjective Optimization of Mechatronic Systems*","date_created":"2020-04-16T08:25:21Z","status":"public","publication_status":"published","publication_identifier":{"issn":["1474-6670"]},"publication":"IFAC Proceedings Volumes","department":[{"_id":"101"}],"author":[{"full_name":"Krüger, Martin","first_name":"Martin","last_name":"Krüger"},{"last_name":"Witting","first_name":"Katrin","full_name":"Witting, Katrin"},{"last_name":"Trächtler","first_name":"Ansgar","full_name":"Trächtler, Ansgar"},{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"}]},{"_id":"10596","intvolume":" 52","issue":"5","year":"2020","citation":{"short":"O. Schütze, O. Cuate, A. Martín, S. Peitz, M. Dellnitz, Engineering Optimization 52 (2020) 832–855.","ieee":"O. Schütze, O. Cuate, A. Martín, S. Peitz, and M. Dellnitz, “Pareto Explorer: a global/local exploration tool for many-objective optimization problems,” Engineering Optimization, vol. 52, no. 5, pp. 832–855, 2020.","chicago":"Schütze, Oliver, Oliver Cuate, Adanay Martín, Sebastian Peitz, and Michael Dellnitz. “Pareto Explorer: A Global/Local Exploration Tool for Many-Objective Optimization Problems.” Engineering Optimization 52, no. 5 (2020): 832–55. https://doi.org/10.1080/0305215x.2019.1617286.","ama":"Schütze O, Cuate O, Martín A, Peitz S, Dellnitz M. Pareto Explorer: a global/local exploration tool for many-objective optimization problems. Engineering Optimization. 2020;52(5):832-855. doi:10.1080/0305215x.2019.1617286","apa":"Schütze, O., Cuate, O., Martín, A., Peitz, S., & Dellnitz, M. (2020). Pareto Explorer: a global/local exploration tool for many-objective optimization problems. Engineering Optimization, 52(5), 832–855. https://doi.org/10.1080/0305215x.2019.1617286","bibtex":"@article{Schütze_Cuate_Martín_Peitz_Dellnitz_2020, title={Pareto Explorer: a global/local exploration tool for many-objective optimization problems}, volume={52}, DOI={10.1080/0305215x.2019.1617286}, number={5}, journal={Engineering Optimization}, author={Schütze, Oliver and Cuate, Oliver and Martín, Adanay and Peitz, Sebastian and Dellnitz, Michael}, year={2020}, pages={832–855} }","mla":"Schütze, Oliver, et al. “Pareto Explorer: A Global/Local Exploration Tool for Many-Objective Optimization Problems.” Engineering Optimization, vol. 52, no. 5, 2020, pp. 832–55, doi:10.1080/0305215x.2019.1617286."},"type":"journal_article","page":"832-855","article_type":"original","abstract":[{"lang":"eng","text":"Multi-objective optimization is an active field of research that has many applications. Owing to its success and because decision-making processes are becoming more and more complex, there is a recent trend for incorporating many objectives into such problems. The challenge with such problems, however, is that the dimensions of the solution sets—the so-called Pareto sets and fronts—grow with the number of objectives. It is thus no longer possible to compute or to approximate the entire solution set of a given problem that contains many (e.g. more than three) objectives. On the other hand, the computation of single solutions (e.g. via scalarization methods) leads to unsatisfying results in many cases, even if user preferences are incorporated. In this article, the Pareto Explorer tool is presented—a global/local exploration tool for the treatment of many-objective optimization problems (MaOPs). In the first step, a solution of the problem is computed via a global search algorithm that ideally already includes user preferences. In the second step, a local search along the Pareto set/front of the given MaOP is performed in user specified directions. For this, several continuation-like procedures are proposed that can incorporate preferences defined in decision, objective, or in weight space. The applicability and usefulness of Pareto Explorer is demonstrated on benchmark problems as well as on an application from industrial laundry design."}],"user_id":"47427","author":[{"last_name":"Schütze","full_name":"Schütze, Oliver","first_name":"Oliver"},{"last_name":"Cuate","first_name":"Oliver","full_name":"Cuate, Oliver"},{"last_name":"Martín","full_name":"Martín, Adanay","first_name":"Adanay"},{"last_name":"Peitz","id":"47427","first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"}],"publication":"Engineering Optimization","status":"public","date_created":"2019-07-10T08:14:39Z","volume":52,"date_updated":"2022-01-06T06:50:46Z","doi":"10.1080/0305215x.2019.1617286","language":[{"iso":"eng"}],"title":"Pareto Explorer: a global/local exploration tool for many-objective optimization problems","department":[{"_id":"101"}],"publication_identifier":{"issn":["0305-215X","1029-0273"]},"publication_status":"published"},{"type":"conference","year":"2015","citation":{"apa":"Keuck, L., Frohleke, N., Bocker, J., & Ziessler, A. (2015). PFC-control for improved inductor utilization. In 2015 17th European Conference on Power Electronics and Applications (EPE’15 ECCE-Europe). https://doi.org/10.1109/epe.2015.7309373","ama":"Keuck L, Frohleke N, Bocker J, Ziessler A. PFC-control for improved inductor utilization. In: 2015 17th European Conference on Power Electronics and Applications (EPE’15 ECCE-Europe). ; 2015. doi:10.1109/epe.2015.7309373","chicago":"Keuck, L., N. Frohleke, J. Bocker, and A. Ziessler. “PFC-Control for Improved Inductor Utilization.” In 2015 17th European Conference on Power Electronics and Applications (EPE’15 ECCE-Europe), 2015. https://doi.org/10.1109/epe.2015.7309373.","bibtex":"@inproceedings{Keuck_Frohleke_Bocker_Ziessler_2015, title={PFC-control for improved inductor utilization}, DOI={10.1109/epe.2015.7309373}, booktitle={2015 17th European Conference on Power Electronics and Applications (EPE’15 ECCE-Europe)}, author={Keuck, L. and Frohleke, N. and Bocker, J. and Ziessler, A.}, year={2015} }","mla":"Keuck, L., et al. “PFC-Control for Improved Inductor Utilization.” 2015 17th European Conference on Power Electronics and Applications (EPE’15 ECCE-Europe), 2015, doi:10.1109/epe.2015.7309373.","short":"L. Keuck, N. Frohleke, J. Bocker, A. Ziessler, in: 2015 17th European Conference on Power Electronics and Applications (EPE’15 ECCE-Europe), 2015.","ieee":"L. Keuck, N. Frohleke, J. Bocker, and A. Ziessler, “PFC-control for improved inductor utilization,” in 2015 17th European Conference on Power Electronics and Applications (EPE’15 ECCE-Europe), 2015."},"doi":"10.1109/epe.2015.7309373","_id":"16622","date_updated":"2022-01-06T06:52:53Z","publication_status":"published","publication_identifier":{"isbn":["9789075815221"]},"status":"public","date_created":"2020-04-16T08:15:10Z","author":[{"last_name":"Keuck","first_name":"L.","full_name":"Keuck, L."},{"last_name":"Frohleke","first_name":"N.","full_name":"Frohleke, N."},{"full_name":"Bocker, J.","first_name":"J.","last_name":"Bocker"},{"last_name":"Ziessler","first_name":"A.","full_name":"Ziessler, A."}],"department":[{"_id":"101"}],"publication":"2015 17th European Conference on Power Electronics and Applications (EPE'15 ECCE-Europe)","title":"PFC-control for improved inductor utilization","user_id":"15701"},{"language":[{"iso":"eng"}],"type":"conference","year":"2018","citation":{"bibtex":"@inproceedings{Beermann_Dellnitz_Peitz_Volkwein_2018, title={POD-based multiobjective optimal control of PDEs with non-smooth objectives}, DOI={10.1002/pamm.201710015}, booktitle={PAMM}, author={Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}, year={2018}, pages={51–54} }","mla":"Beermann, Dennis, et al. “POD-Based Multiobjective Optimal Control of PDEs with Non-Smooth Objectives.” PAMM, 2018, pp. 51–54, doi:10.1002/pamm.201710015.","ama":"Beermann D, Dellnitz M, Peitz S, Volkwein S. POD-based multiobjective optimal control of PDEs with non-smooth objectives. In: PAMM. ; 2018:51-54. doi:10.1002/pamm.201710015","apa":"Beermann, D., Dellnitz, M., Peitz, S., & Volkwein, S. (2018). POD-based multiobjective optimal control of PDEs with non-smooth objectives. In PAMM (pp. 51–54). https://doi.org/10.1002/pamm.201710015","chicago":"Beermann, Dennis, Michael Dellnitz, Sebastian Peitz, and Stefan Volkwein. “POD-Based Multiobjective Optimal Control of PDEs with Non-Smooth Objectives.” In PAMM, 51–54, 2018. https://doi.org/10.1002/pamm.201710015.","ieee":"D. Beermann, M. Dellnitz, S. Peitz, and S. Volkwein, “POD-based multiobjective optimal control of PDEs with non-smooth objectives,” in PAMM, 2018, pp. 51–54.","short":"D. Beermann, M. Dellnitz, S. Peitz, S. Volkwein, in: PAMM, 2018, pp. 51–54."},"page":"51-54","date_updated":"2022-01-06T07:04:00Z","_id":"8757","doi":"10.1002/pamm.201710015","author":[{"last_name":"Beermann","full_name":"Beermann, Dennis","first_name":"Dennis"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"last_name":"Peitz","id":"47427","first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian"},{"last_name":"Volkwein","first_name":"Stefan","full_name":"Volkwein, Stefan"}],"department":[{"_id":"101"}],"publication":"PAMM","status":"public","date_created":"2019-03-29T13:34:25Z","project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"publication_status":"published","publication_identifier":{"issn":["1617-7061"]},"abstract":[{"text":"A framework for set‐oriented multiobjective optimal control of partial differential equations using reduced order modeling has recently been developed [1]. Following concepts from localized reduced bases methods, error estimators for the reduced cost functionals are utilized to construct a library of locally valid reduced order models. This way, a superset of the Pareto set can efficiently be computed while maintaining a prescribed error bound. In this article, this algorithm is applied to a problem with non‐smooth objective functionals. Using an academic example, we show that the extension to non‐smooth problems can be realized in a straightforward manner. We then discuss the implications on the numerical results.","lang":"eng"}],"user_id":"47427","title":"POD-based multiobjective optimal control of PDEs with non-smooth objectives"},{"year":"2018","type":"journal_article","citation":{"bibtex":"@article{Hruska_Abella_Nüske_Kavraki_Clementi_2018, title={Quantitative comparison of adaptive sampling methods for protein dynamics}, DOI={10.1063/1.5053582}, number={244119}, journal={The Journal of Chemical Physics}, author={Hruska, Eugen and Abella, Jayvee R. and Nüske, Feliks and Kavraki, Lydia E. and Clementi, Cecilia}, year={2018} }","mla":"Hruska, Eugen, et al. “Quantitative Comparison of Adaptive Sampling Methods for Protein Dynamics.” The Journal of Chemical Physics, 244119, 2018, doi:10.1063/1.5053582.","chicago":"Hruska, Eugen, Jayvee R. Abella, Feliks Nüske, Lydia E. Kavraki, and Cecilia Clementi. “Quantitative Comparison of Adaptive Sampling Methods for Protein Dynamics.” The Journal of Chemical Physics, 2018. https://doi.org/10.1063/1.5053582.","ama":"Hruska E, Abella JR, Nüske F, Kavraki LE, Clementi C. Quantitative comparison of adaptive sampling methods for protein dynamics. The Journal of Chemical Physics. 2018. doi:10.1063/1.5053582","apa":"Hruska, E., Abella, J. R., Nüske, F., Kavraki, L. E., & Clementi, C. (2018). Quantitative comparison of adaptive sampling methods for protein dynamics. The Journal of Chemical Physics. https://doi.org/10.1063/1.5053582","ieee":"E. Hruska, J. R. Abella, F. Nüske, L. E. Kavraki, and C. Clementi, “Quantitative comparison of adaptive sampling methods for protein dynamics,” The Journal of Chemical Physics, 2018.","short":"E. Hruska, J.R. Abella, F. Nüske, L.E. Kavraki, C. Clementi, The Journal of Chemical Physics (2018)."},"language":[{"iso":"eng"}],"doi":"10.1063/1.5053582","article_number":"244119","_id":"21943","date_updated":"2022-01-06T06:55:20Z","publication_identifier":{"issn":["0021-9606","1089-7690"]},"publication_status":"published","date_created":"2021-04-30T17:00:24Z","status":"public","department":[{"_id":"101"}],"publication":"The Journal of Chemical Physics","author":[{"full_name":"Hruska, Eugen","first_name":"Eugen","last_name":"Hruska"},{"full_name":"Abella, Jayvee R.","first_name":"Jayvee R.","last_name":"Abella"},{"full_name":"Nüske, Feliks","orcid":"0000-0003-2444-7889","first_name":"Feliks","id":"81513","last_name":"Nüske"},{"last_name":"Kavraki","first_name":"Lydia E.","full_name":"Kavraki, Lydia E."},{"full_name":"Clementi, Cecilia","first_name":"Cecilia","last_name":"Clementi"}],"title":"Quantitative comparison of adaptive sampling methods for protein dynamics","user_id":"81513","extern":"1"},{"language":[{"iso":"eng"}],"page":"2771-2783","type":"journal_article","citation":{"chicago":"Litzinger, Florian, Lorenzo Boninsegna, Hao Wu, Feliks Nüske, Raajen Patel, Richard Baraniuk, Frank Noé, and Cecilia Clementi. “Rapid Calculation of Molecular Kinetics Using Compressed Sensing.” Journal of Chemical Theory and Computation, 2018, 2771–83. https://doi.org/10.1021/acs.jctc.8b00089.","ama":"Litzinger F, Boninsegna L, Wu H, et al. Rapid Calculation of Molecular Kinetics Using Compressed Sensing. Journal of Chemical Theory and Computation. 2018:2771-2783. doi:10.1021/acs.jctc.8b00089","apa":"Litzinger, F., Boninsegna, L., Wu, H., Nüske, F., Patel, R., Baraniuk, R., … Clementi, C. (2018). Rapid Calculation of Molecular Kinetics Using Compressed Sensing. Journal of Chemical Theory and Computation, 2771–2783. https://doi.org/10.1021/acs.jctc.8b00089","bibtex":"@article{Litzinger_Boninsegna_Wu_Nüske_Patel_Baraniuk_Noé_Clementi_2018, title={Rapid Calculation of Molecular Kinetics Using Compressed Sensing}, DOI={10.1021/acs.jctc.8b00089}, journal={Journal of Chemical Theory and Computation}, author={Litzinger, Florian and Boninsegna, Lorenzo and Wu, Hao and Nüske, Feliks and Patel, Raajen and Baraniuk, Richard and Noé, Frank and Clementi, Cecilia}, year={2018}, pages={2771–2783} }","mla":"Litzinger, Florian, et al. “Rapid Calculation of Molecular Kinetics Using Compressed Sensing.” Journal of Chemical Theory and Computation, 2018, pp. 2771–83, doi:10.1021/acs.jctc.8b00089.","short":"F. Litzinger, L. Boninsegna, H. Wu, F. Nüske, R. Patel, R. Baraniuk, F. Noé, C. Clementi, Journal of Chemical Theory and Computation (2018) 2771–2783.","ieee":"F. Litzinger et al., “Rapid Calculation of Molecular Kinetics Using Compressed Sensing,” Journal of Chemical Theory and Computation, pp. 2771–2783, 2018."},"year":"2018","doi":"10.1021/acs.jctc.8b00089","date_updated":"2022-01-06T06:55:20Z","_id":"21940","date_created":"2021-04-30T16:58:07Z","status":"public","publication_identifier":{"issn":["1549-9618","1549-9626"]},"publication_status":"published","publication":"Journal of Chemical Theory and Computation","department":[{"_id":"101"}],"author":[{"last_name":"Litzinger","first_name":"Florian","full_name":"Litzinger, Florian"},{"last_name":"Boninsegna","full_name":"Boninsegna, Lorenzo","first_name":"Lorenzo"},{"last_name":"Wu","first_name":"Hao","full_name":"Wu, Hao"},{"last_name":"Nüske","id":"81513","first_name":"Feliks","full_name":"Nüske, Feliks","orcid":"0000-0003-2444-7889"},{"last_name":"Patel","full_name":"Patel, Raajen","first_name":"Raajen"},{"full_name":"Baraniuk, Richard","first_name":"Richard","last_name":"Baraniuk"},{"last_name":"Noé","first_name":"Frank","full_name":"Noé, Frank"},{"first_name":"Cecilia","full_name":"Clementi, Cecilia","last_name":"Clementi"}],"user_id":"81513","title":"Rapid Calculation of Molecular Kinetics Using Compressed Sensing","extern":"1"},{"doi":"10.1002/pamm.201510008","date_updated":"2022-01-06T06:52:54Z","_id":"16660","page":"27-30","type":"journal_article","citation":{"apa":"Ringkamp, M., Ober-Blöbaum, S., & Leyendecker, S. (2015). Relaxing mixed integer optimal control problems using a time transformation. PAMM, 27–30. https://doi.org/10.1002/pamm.201510008","ama":"Ringkamp M, Ober-Blöbaum S, Leyendecker S. Relaxing mixed integer optimal control problems using a time transformation. PAMM. 2015:27-30. doi:10.1002/pamm.201510008","chicago":"Ringkamp, Maik, Sina Ober-Blöbaum, and Sigrid Leyendecker. “Relaxing Mixed Integer Optimal Control Problems Using a Time Transformation.” PAMM, 2015, 27–30. https://doi.org/10.1002/pamm.201510008.","mla":"Ringkamp, Maik, et al. “Relaxing Mixed Integer Optimal Control Problems Using a Time Transformation.” PAMM, 2015, pp. 27–30, doi:10.1002/pamm.201510008.","bibtex":"@article{Ringkamp_Ober-Blöbaum_Leyendecker_2015, title={Relaxing mixed integer optimal control problems using a time transformation}, DOI={10.1002/pamm.201510008}, journal={PAMM}, author={Ringkamp, Maik and Ober-Blöbaum, Sina and Leyendecker, Sigrid}, year={2015}, pages={27–30} }","short":"M. Ringkamp, S. Ober-Blöbaum, S. Leyendecker, PAMM (2015) 27–30.","ieee":"M. Ringkamp, S. Ober-Blöbaum, and S. Leyendecker, “Relaxing mixed integer optimal control problems using a time transformation,” PAMM, pp. 27–30, 2015."},"year":"2015","language":[{"iso":"eng"}],"title":"Relaxing mixed integer optimal control problems using a time transformation","user_id":"15701","publication_identifier":{"issn":["1617-7061"]},"publication_status":"published","date_created":"2020-04-16T09:52:20Z","status":"public","department":[{"_id":"101"}],"publication":"PAMM","author":[{"first_name":"Maik","full_name":"Ringkamp, Maik","last_name":"Ringkamp"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"first_name":"Sigrid","full_name":"Leyendecker, Sigrid","last_name":"Leyendecker"}]},{"title":"Return Time Dynamics as a Tool for Finding Almost Invariant Sets","user_id":"15701","publication_identifier":{"issn":["0077-8923"]},"publication_status":"published","status":"public","date_created":"2020-04-16T10:10:57Z","author":[{"full_name":"Thiere, B.","first_name":"B.","last_name":"Thiere"}],"publication":"Annals of the New York Academy of Sciences","department":[{"_id":"101"}],"doi":"10.1196/annals.1370.027","_id":"16674","date_updated":"2022-01-06T06:52:54Z","year":"2006","citation":{"short":"B. Thiere, Annals of the New York Academy of Sciences (2006) 44–54.","ieee":"B. Thiere, “Return Time Dynamics as a Tool for Finding Almost Invariant Sets,” Annals of the New York Academy of Sciences, pp. 44–54, 2006.","chicago":"Thiere, B. “Return Time Dynamics as a Tool for Finding Almost Invariant Sets.” Annals of the New York Academy of Sciences, 2006, 44–54. https://doi.org/10.1196/annals.1370.027.","ama":"Thiere B. Return Time Dynamics as a Tool for Finding Almost Invariant Sets. Annals of the New York Academy of Sciences. 2006:44-54. doi:10.1196/annals.1370.027","apa":"Thiere, B. (2006). Return Time Dynamics as a Tool for Finding Almost Invariant Sets. Annals of the New York Academy of Sciences, 44–54. https://doi.org/10.1196/annals.1370.027","mla":"Thiere, B. “Return Time Dynamics as a Tool for Finding Almost Invariant Sets.” Annals of the New York Academy of Sciences, 2006, pp. 44–54, doi:10.1196/annals.1370.027.","bibtex":"@article{Thiere_2006, title={Return Time Dynamics as a Tool for Finding Almost Invariant Sets}, DOI={10.1196/annals.1370.027}, journal={Annals of the New York Academy of Sciences}, author={Thiere, B.}, year={2006}, pages={44–54} }"},"type":"journal_article","page":"44-54","language":[{"iso":"eng"}]},{"oa":"1","date_updated":"2022-06-20T13:17:53Z","_id":"16711","type":"preprint","citation":{"bibtex":"@article{Gerlach_Koltai_Dellnitz_2019, title={Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems}, journal={arXiv:1902.08824}, author={Gerlach, Raphael and Koltai, Péter and Dellnitz, Michael}, year={2019} }","mla":"Gerlach, Raphael, et al. “Revealing the Intrinsic Geometry of Finite Dimensional Invariant Sets of Infinite Dimensional Dynamical Systems.” ArXiv:1902.08824, 2019.","ieee":"R. Gerlach, P. Koltai, and M. Dellnitz, “Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems,” arXiv:1902.08824. 2019.","chicago":"Gerlach, Raphael, Péter Koltai, and Michael Dellnitz. “Revealing the Intrinsic Geometry of Finite Dimensional Invariant Sets of Infinite Dimensional Dynamical Systems.” ArXiv:1902.08824, 2019.","short":"R. Gerlach, P. Koltai, M. Dellnitz, ArXiv:1902.08824 (2019).","apa":"Gerlach, R., Koltai, P., & Dellnitz, M. (2019). Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems. In arXiv:1902.08824.","ama":"Gerlach R, Koltai P, Dellnitz M. Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems. arXiv:190208824. Published online 2019."},"year":"2019","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1902.08824"}],"title":"Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems","ddc":["510"],"user_id":"32655","abstract":[{"lang":"eng","text":"Embedding techniques allow the approximations of finite dimensional\r\nattractors and manifolds of infinite dimensional dynamical systems via\r\nsubdivision and continuation methods. These approximations give a topological\r\none-to-one image of the original set. In order to additionally reveal their\r\ngeometry we use diffusion mapst o find intrinsic coordinates. We illustrate our\r\nresults on the unstable manifold of the one-dimensional Kuramoto--Sivashinsky\r\nequation, as well as for the attractor of the Mackey-Glass delay differential\r\nequation."}],"status":"public","has_accepted_license":"1","date_created":"2020-04-16T14:06:21Z","author":[{"full_name":"Gerlach, Raphael","first_name":"Raphael","id":"32655","last_name":"Gerlach"},{"last_name":"Koltai","full_name":"Koltai, Péter","first_name":"Péter"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"publication":"arXiv:1902.08824","department":[{"_id":"101"}]},{"title":"Rigorous computation of topological entropy with respect to a finite partition","user_id":"15701","author":[{"last_name":"Froyland","first_name":"Gary","full_name":"Froyland, Gary"},{"full_name":"Junge, Oliver","first_name":"Oliver","last_name":"Junge"},{"last_name":"Ochs","full_name":"Ochs, Gunter","first_name":"Gunter"}],"department":[{"_id":"101"}],"publication":"Physica D: Nonlinear Phenomena","publication_status":"published","publication_identifier":{"issn":["0167-2789"]},"status":"public","date_created":"2020-04-16T06:08:12Z","_id":"16601","date_updated":"2022-01-06T06:52:53Z","doi":"10.1016/s0167-2789(01)00216-0","type":"journal_article","citation":{"chicago":"Froyland, Gary, Oliver Junge, and Gunter Ochs. “Rigorous Computation of Topological Entropy with Respect to a Finite Partition.” Physica D: Nonlinear Phenomena, 2001, 68–84. https://doi.org/10.1016/s0167-2789(01)00216-0.","apa":"Froyland, G., Junge, O., & Ochs, G. (2001). Rigorous computation of topological entropy with respect to a finite partition. Physica D: Nonlinear Phenomena, 68–84. https://doi.org/10.1016/s0167-2789(01)00216-0","ama":"Froyland G, Junge O, Ochs G. Rigorous computation of topological entropy with respect to a finite partition. Physica D: Nonlinear Phenomena. 2001:68-84. doi:10.1016/s0167-2789(01)00216-0","bibtex":"@article{Froyland_Junge_Ochs_2001, title={Rigorous computation of topological entropy with respect to a finite partition}, DOI={10.1016/s0167-2789(01)00216-0}, journal={Physica D: Nonlinear Phenomena}, author={Froyland, Gary and Junge, Oliver and Ochs, Gunter}, year={2001}, pages={68–84} }","mla":"Froyland, Gary, et al. “Rigorous Computation of Topological Entropy with Respect to a Finite Partition.” Physica D: Nonlinear Phenomena, 2001, pp. 68–84, doi:10.1016/s0167-2789(01)00216-0.","short":"G. Froyland, O. Junge, G. Ochs, Physica D: Nonlinear Phenomena (2001) 68–84.","ieee":"G. Froyland, O. Junge, and G. Ochs, “Rigorous computation of topological entropy with respect to a finite partition,” Physica D: Nonlinear Phenomena, pp. 68–84, 2001."},"year":"2001","page":"68-84","language":[{"iso":"eng"}]},{"_id":"16616","date_updated":"2022-01-06T06:52:53Z","doi":"10.1142/9789812792617_0178","year":"2000","citation":{"ieee":"O. Junge, “Rigorous discretization of subdivision techniques,” in Equadiff 99, 2000.","short":"O. Junge, in: Equadiff 99, 2000.","mla":"Junge, Oliver. “Rigorous Discretization of Subdivision Techniques.” Equadiff 99, 2000, doi:10.1142/9789812792617_0178.","bibtex":"@inbook{Junge_2000, title={Rigorous discretization of subdivision techniques}, DOI={10.1142/9789812792617_0178}, booktitle={Equadiff 99}, author={Junge, Oliver}, year={2000} }","ama":"Junge O. Rigorous discretization of subdivision techniques. In: Equadiff 99. ; 2000. doi:10.1142/9789812792617_0178","apa":"Junge, O. (2000). Rigorous discretization of subdivision techniques. In Equadiff 99. https://doi.org/10.1142/9789812792617_0178","chicago":"Junge, Oliver. “Rigorous Discretization of Subdivision Techniques.” In Equadiff 99, 2000. https://doi.org/10.1142/9789812792617_0178."},"type":"book_chapter","language":[{"iso":"eng"}],"title":"Rigorous discretization of subdivision techniques","user_id":"15701","department":[{"_id":"101"}],"publication":"Equadiff 99","author":[{"full_name":"Junge, Oliver","first_name":"Oliver","last_name":"Junge"}],"publication_identifier":{"isbn":["9789810243593","9789812792617"]},"publication_status":"published","date_created":"2020-04-16T08:07:52Z","status":"public"},{"_id":"16296","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/1906.09075.pdf"}],"year":"2022","type":"book_chapter","citation":{"bibtex":"@inbook{Banholzer_Gebken_Dellnitz_Peitz_Volkwein_2022, place={Cham}, title={ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation}, DOI={10.1007/978-3-030-79393-7_3}, booktitle={Non-Smooth and Complementarity-Based Distributed Parameter Systems}, publisher={Springer}, author={Banholzer, Stefan and Gebken, Bennet and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}, editor={Michael, Hintermüller and Roland, Herzog and Christian, Kanzow and Michael, Ulbrich and Stefan, Ulbrich}, year={2022}, pages={43–76} }","mla":"Banholzer, Stefan, et al. “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation.” Non-Smooth and Complementarity-Based Distributed Parameter Systems, edited by Hintermüller Michael et al., Springer, 2022, pp. 43–76, doi:10.1007/978-3-030-79393-7_3.","ama":"Banholzer S, Gebken B, Dellnitz M, Peitz S, Volkwein S. ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation. In: Michael H, Roland H, Christian K, Michael U, Stefan U, eds. Non-Smooth and Complementarity-Based Distributed Parameter Systems. Springer; 2022:43-76. doi:10.1007/978-3-030-79393-7_3","apa":"Banholzer, S., Gebken, B., Dellnitz, M., Peitz, S., & Volkwein, S. (2022). ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation. In H. Michael, H. Roland, K. Christian, U. Michael, & U. Stefan (Eds.), Non-Smooth and Complementarity-Based Distributed Parameter Systems (pp. 43–76). Springer. https://doi.org/10.1007/978-3-030-79393-7_3","chicago":"Banholzer, Stefan, Bennet Gebken, Michael Dellnitz, Sebastian Peitz, and Stefan Volkwein. “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation.” In Non-Smooth and Complementarity-Based Distributed Parameter Systems, edited by Hintermüller Michael, Herzog Roland, Kanzow Christian, Ulbrich Michael, and Ulbrich Stefan, 43–76. Cham: Springer, 2022. https://doi.org/10.1007/978-3-030-79393-7_3.","ieee":"S. Banholzer, B. Gebken, M. Dellnitz, S. Peitz, and S. Volkwein, “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation,” in Non-Smooth and Complementarity-Based Distributed Parameter Systems, H. Michael, H. Roland, K. Christian, U. Michael, and U. Stefan, Eds. Cham: Springer, 2022, pp. 43–76.","short":"S. Banholzer, B. Gebken, M. Dellnitz, S. Peitz, S. Volkwein, in: H. Michael, H. Roland, K. Christian, U. Michael, U. Stefan (Eds.), Non-Smooth and Complementarity-Based Distributed Parameter Systems, Springer, Cham, 2022, pp. 43–76."},"page":"43-76","abstract":[{"text":"Multiobjective optimization plays an increasingly important role in modern\r\napplications, where several objectives are often of equal importance. The task\r\nin multiobjective optimization and multiobjective optimal control is therefore\r\nto compute the set of optimal compromises (the Pareto set) between the\r\nconflicting objectives. Since the Pareto set generally consists of an infinite\r\nnumber of solutions, the computational effort can quickly become challenging\r\nwhich is particularly problematic when the objectives are costly to evaluate as\r\nis the case for models governed by partial differential equations (PDEs). To\r\ndecrease the numerical effort to an affordable amount, surrogate models can be\r\nused to replace the expensive PDE evaluations. Existing multiobjective\r\noptimization methods using model reduction are limited either to low parameter\r\ndimensions or to few (ideally two) objectives. In this article, we present a\r\ncombination of the reduced basis model reduction method with a continuation\r\napproach using inexact gradients. The resulting approach can handle an\r\narbitrary number of objectives while yielding a significant reduction in\r\ncomputing time.","lang":"eng"}],"user_id":"47427","author":[{"full_name":"Banholzer, Stefan","first_name":"Stefan","last_name":"Banholzer"},{"first_name":"Bennet","full_name":"Gebken, Bennet","last_name":"Gebken","id":"32643"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"full_name":"Peitz, Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","first_name":"Sebastian","id":"47427","last_name":"Peitz"},{"full_name":"Volkwein, Stefan","first_name":"Stefan","last_name":"Volkwein"}],"publisher":"Springer","publication":"Non-Smooth and Complementarity-Based Distributed Parameter Systems","status":"public","date_created":"2020-03-13T12:45:31Z","date_updated":"2022-03-14T13:04:51Z","oa":"1","doi":"10.1007/978-3-030-79393-7_3","language":[{"iso":"eng"}],"place":"Cham","title":"ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation","department":[{"_id":"101"},{"_id":"655"}],"editor":[{"first_name":"Hintermüller","full_name":"Michael, Hintermüller","last_name":"Michael"},{"last_name":"Roland","first_name":"Herzog","full_name":"Roland, Herzog"},{"first_name":"Kanzow","full_name":"Christian, Kanzow","last_name":"Christian"},{"last_name":"Michael","first_name":"Ulbrich","full_name":"Michael, Ulbrich"},{"last_name":"Stefan","full_name":"Stefan, Ulbrich","first_name":"Ulbrich"}],"publication_identifier":{"isbn":["978-3-030-79392-0"]}},{"year":"2013","type":"conference","citation":{"mla":"Jakobsmeyer, R., et al. “Running Performance Analysis in Basketball Using Recorded Trajectory Data.” Performance Analysis of Sport IX, Part 8, Routledge, 2013.","bibtex":"@inproceedings{Jakobsmeyer_Schnittker_Timmermann_Zorn_Rückert_Baumeister_2013, title={Running performance analysis in basketball using recorded trajectory data}, booktitle={Performance Analysis of Sport IX, Part 8, Routledge}, author={Jakobsmeyer, R. and Schnittker, R. and Timmermann, R. and Zorn, R. and Rückert, U. and Baumeister, J.}, year={2013} }","chicago":"Jakobsmeyer, R., R. Schnittker, R. Timmermann, R. Zorn, U. Rückert, and J. Baumeister. “Running Performance Analysis in Basketball Using Recorded Trajectory Data.” In Performance Analysis of Sport IX, Part 8, Routledge, 2013.","ama":"Jakobsmeyer R, Schnittker R, Timmermann R, Zorn R, Rückert U, Baumeister J. Running performance analysis in basketball using recorded trajectory data. In: Performance Analysis of Sport IX, Part 8, Routledge. ; 2013.","apa":"Jakobsmeyer, R., Schnittker, R., Timmermann, R., Zorn, R., Rückert, U., & Baumeister, J. (2013). Running performance analysis in basketball using recorded trajectory data. In Performance Analysis of Sport IX, Part 8, Routledge.","ieee":"R. Jakobsmeyer, R. Schnittker, R. Timmermann, R. Zorn, U. Rückert, and J. Baumeister, “Running performance analysis in basketball using recorded trajectory data,” in Performance Analysis of Sport IX, Part 8, Routledge, 2013.","short":"R. Jakobsmeyer, R. Schnittker, R. Timmermann, R. Zorn, U. Rückert, J. Baumeister, in: Performance Analysis of Sport IX, Part 8, Routledge, 2013."},"language":[{"iso":"eng"}],"_id":"17049","date_updated":"2022-01-06T06:53:03Z","date_created":"2020-05-20T08:43:32Z","status":"public","department":[{"_id":"101"}],"publication":"Performance Analysis of Sport IX, Part 8, Routledge","author":[{"last_name":"Jakobsmeyer","full_name":"Jakobsmeyer, R.","first_name":"R."},{"last_name":"Schnittker","first_name":"R.","full_name":"Schnittker, R."},{"last_name":"Timmermann","first_name":"R.","full_name":"Timmermann, R."},{"last_name":"Zorn","full_name":"Zorn, R.","first_name":"R."},{"last_name":"Rückert","first_name":"U.","full_name":"Rückert, U."},{"first_name":"J.","full_name":"Baumeister, J.","last_name":"Baumeister"}],"title":"Running performance analysis in basketball using recorded trajectory data","user_id":"47427"},{"user_id":"15701","title":"Satellite Formation, a Mobile Sensor Network in Space","author":[{"last_name":"Krishnamurthy","first_name":"A.","full_name":"Krishnamurthy, A."},{"last_name":"Preis","full_name":"Preis, R.","first_name":"R."}],"publication":"19th IEEE International Parallel and Distributed Processing Symposium","department":[{"_id":"101"}],"status":"public","date_created":"2020-04-16T08:22:43Z","publication_status":"published","publication_identifier":{"isbn":["0769523129"]},"date_updated":"2022-01-06T06:52:53Z","_id":"16628","doi":"10.1109/ipdps.2005.387","year":"2005","type":"conference","citation":{"short":"A. Krishnamurthy, R. Preis, in: 19th IEEE International Parallel and Distributed Processing Symposium, 2005.","ieee":"A. Krishnamurthy and R. Preis, “Satellite Formation, a Mobile Sensor Network in Space,” in 19th IEEE International Parallel and Distributed Processing Symposium, 2005.","apa":"Krishnamurthy, A., & Preis, R. (2005). Satellite Formation, a Mobile Sensor Network in Space. In 19th IEEE International Parallel and Distributed Processing Symposium. https://doi.org/10.1109/ipdps.2005.387","ama":"Krishnamurthy A, Preis R. Satellite Formation, a Mobile Sensor Network in Space. In: 19th IEEE International Parallel and Distributed Processing Symposium. ; 2005. doi:10.1109/ipdps.2005.387","chicago":"Krishnamurthy, A., and R. Preis. “Satellite Formation, a Mobile Sensor Network in Space.” In 19th IEEE International Parallel and Distributed Processing Symposium, 2005. https://doi.org/10.1109/ipdps.2005.387.","mla":"Krishnamurthy, A., and R. Preis. “Satellite Formation, a Mobile Sensor Network in Space.” 19th IEEE International Parallel and Distributed Processing Symposium, 2005, doi:10.1109/ipdps.2005.387.","bibtex":"@inproceedings{Krishnamurthy_Preis_2005, title={Satellite Formation, a Mobile Sensor Network in Space}, DOI={10.1109/ipdps.2005.387}, booktitle={19th IEEE International Parallel and Distributed Processing Symposium}, author={Krishnamurthy, A. and Preis, R.}, year={2005} }"}},{"title":"Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators","user_id":"15701","author":[{"full_name":"Dellnitz, M.","first_name":"M.","last_name":"Dellnitz"},{"first_name":"G.","full_name":"Froyland, G.","last_name":"Froyland"},{"first_name":"C.","full_name":"Horenkamp, C.","last_name":"Horenkamp"},{"full_name":"Padberg-Gehle, K.","first_name":"K.","last_name":"Padberg-Gehle"},{"last_name":"Sen Gupta","full_name":"Sen Gupta, A.","first_name":"A."}],"department":[{"_id":"101"}],"publication":"Nonlinear Processes in Geophysics","publication_status":"published","publication_identifier":{"issn":["1607-7946"]},"status":"public","date_created":"2020-04-16T05:03:56Z","date_updated":"2022-01-06T06:52:52Z","_id":"16573","doi":"10.5194/npg-16-655-2009","citation":{"ieee":"M. Dellnitz, G. Froyland, C. Horenkamp, K. Padberg-Gehle, and A. Sen Gupta, “Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators,” Nonlinear Processes in Geophysics, pp. 655–663, 2009.","short":"M. Dellnitz, G. Froyland, C. Horenkamp, K. Padberg-Gehle, A. Sen Gupta, Nonlinear Processes in Geophysics (2009) 655–663.","bibtex":"@article{Dellnitz_Froyland_Horenkamp_Padberg-Gehle_Sen Gupta_2009, title={Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators}, DOI={10.5194/npg-16-655-2009}, journal={Nonlinear Processes in Geophysics}, author={Dellnitz, M. and Froyland, G. and Horenkamp, C. and Padberg-Gehle, K. and Sen Gupta, A.}, year={2009}, pages={655–663} }","mla":"Dellnitz, M., et al. “Seasonal Variability of the Subpolar Gyres in the Southern Ocean: A Numerical Investigation Based on Transfer Operators.” Nonlinear Processes in Geophysics, 2009, pp. 655–63, doi:10.5194/npg-16-655-2009.","chicago":"Dellnitz, M., G. Froyland, C. Horenkamp, K. Padberg-Gehle, and A. Sen Gupta. “Seasonal Variability of the Subpolar Gyres in the Southern Ocean: A Numerical Investigation Based on Transfer Operators.” Nonlinear Processes in Geophysics, 2009, 655–63. https://doi.org/10.5194/npg-16-655-2009.","ama":"Dellnitz M, Froyland G, Horenkamp C, Padberg-Gehle K, Sen Gupta A. Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics. 2009:655-663. doi:10.5194/npg-16-655-2009","apa":"Dellnitz, M., Froyland, G., Horenkamp, C., Padberg-Gehle, K., & Sen Gupta, A. (2009). Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 655–663. https://doi.org/10.5194/npg-16-655-2009"},"type":"journal_article","year":"2009","page":"655-663","language":[{"iso":"eng"}]},{"publication":"7th International Heinz Nixdorf Symposium: Self-optimizing Mechatronic Systems: Designing the Future","department":[{"_id":"101"}],"author":[{"last_name":"Geisler","first_name":"Jens","full_name":"Geisler, Jens"},{"first_name":"Katrin","full_name":"Witting, Katrin","last_name":"Witting"},{"last_name":"Trächtler","full_name":"Trächtler, Ansgar","first_name":"Ansgar"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"}],"date_created":"2020-05-20T07:40:22Z","status":"public","user_id":"47427","title":"Self-Optimization of the Guidance Module of a Rail-bound Vehicle","language":[{"iso":"eng"}],"citation":{"chicago":"Geisler, Jens, Katrin Witting, Ansgar Trächtler, and Michael Dellnitz. “Self-Optimization of the Guidance Module of a Rail-Bound Vehicle.” In 7th International Heinz Nixdorf Symposium: Self-Optimizing Mechatronic Systems: Designing the Future, 2008.","ama":"Geisler J, Witting K, Trächtler A, Dellnitz M. Self-Optimization of the Guidance Module of a Rail-bound Vehicle. In: 7th International Heinz Nixdorf Symposium: Self-Optimizing Mechatronic Systems: Designing the Future. ; 2008.","apa":"Geisler, J., Witting, K., Trächtler, A., & Dellnitz, M. (2008). Self-Optimization of the Guidance Module of a Rail-bound Vehicle. In 7th International Heinz Nixdorf Symposium: Self-optimizing Mechatronic Systems: Designing the Future.","mla":"Geisler, Jens, et al. “Self-Optimization of the Guidance Module of a Rail-Bound Vehicle.” 7th International Heinz Nixdorf Symposium: Self-Optimizing Mechatronic Systems: Designing the Future, 2008.","bibtex":"@inproceedings{Geisler_Witting_Trächtler_Dellnitz_2008, title={Self-Optimization of the Guidance Module of a Rail-bound Vehicle}, booktitle={7th International Heinz Nixdorf Symposium: Self-optimizing Mechatronic Systems: Designing the Future}, author={Geisler, Jens and Witting, Katrin and Trächtler, Ansgar and Dellnitz, Michael}, year={2008} }","short":"J. Geisler, K. Witting, A. Trächtler, M. Dellnitz, in: 7th International Heinz Nixdorf Symposium: Self-Optimizing Mechatronic Systems: Designing the Future, 2008.","ieee":"J. Geisler, K. Witting, A. Trächtler, and M. Dellnitz, “Self-Optimization of the Guidance Module of a Rail-bound Vehicle,” in 7th International Heinz Nixdorf Symposium: Self-optimizing Mechatronic Systems: Designing the Future, 2008."},"type":"conference","year":"2008","_id":"17031","date_updated":"2022-01-06T06:53:02Z"},{"department":[{"_id":"101"}],"publication":"Dynamical Systems","author":[{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"last_name":"Klus","first_name":"Stefan","full_name":"Klus, Stefan"}],"date_created":"2020-04-15T08:40:29Z","status":"public","publication_identifier":{"issn":["1468-9367","1468-9375"]},"publication_status":"published","user_id":"15701","title":"Sensing and control in symmetric networks","language":[{"iso":"eng"}],"page":"61-79","year":"2017","type":"journal_article","citation":{"chicago":"Dellnitz, Michael, and Stefan Klus. “Sensing and Control in Symmetric Networks.” Dynamical Systems, 2017, 61–79. https://doi.org/10.1080/14689367.2016.1215410.","ama":"Dellnitz M, Klus S. Sensing and control in symmetric networks. Dynamical Systems. 2017:61-79. doi:10.1080/14689367.2016.1215410","apa":"Dellnitz, M., & Klus, S. (2017). Sensing and control in symmetric networks. Dynamical Systems, 61–79. https://doi.org/10.1080/14689367.2016.1215410","mla":"Dellnitz, Michael, and Stefan Klus. “Sensing and Control in Symmetric Networks.” Dynamical Systems, 2017, pp. 61–79, doi:10.1080/14689367.2016.1215410.","bibtex":"@article{Dellnitz_Klus_2017, title={Sensing and control in symmetric networks}, DOI={10.1080/14689367.2016.1215410}, journal={Dynamical Systems}, author={Dellnitz, Michael and Klus, Stefan}, year={2017}, pages={61–79} }","short":"M. Dellnitz, S. Klus, Dynamical Systems (2017) 61–79.","ieee":"M. Dellnitz and S. Klus, “Sensing and control in symmetric networks,” Dynamical Systems, pp. 61–79, 2017."},"_id":"16540","date_updated":"2022-01-06T06:52:52Z","doi":"10.1080/14689367.2016.1215410"},{"year":"2007","type":"conference","citation":{"short":"M. Dellnitz, K. Padberg, M. Post, B. Thiere, in: AIP Conference Proceedings, 2007.","ieee":"M. Dellnitz, K. Padberg, M. Post, and B. Thiere, “Set Oriented Approximation of Invariant Manifolds: Review of Concepts for Astrodynamical Problems,” in AIP Conference Proceedings, 2007.","ama":"Dellnitz M, Padberg K, Post M, Thiere B. Set Oriented Approximation of Invariant Manifolds: Review of Concepts for Astrodynamical Problems. In: AIP Conference Proceedings. ; 2007. doi:10.1063/1.2710046","apa":"Dellnitz, M., Padberg, K., Post, M., & Thiere, B. (2007). Set Oriented Approximation of Invariant Manifolds: Review of Concepts for Astrodynamical Problems. In AIP Conference Proceedings. https://doi.org/10.1063/1.2710046","chicago":"Dellnitz, Michael, Kathrin Padberg, Marcus Post, and Bianca Thiere. “Set Oriented Approximation of Invariant Manifolds: Review of Concepts for Astrodynamical Problems.” In AIP Conference Proceedings, 2007. https://doi.org/10.1063/1.2710046.","mla":"Dellnitz, Michael, et al. “Set Oriented Approximation of Invariant Manifolds: Review of Concepts for Astrodynamical Problems.” AIP Conference Proceedings, 2007, doi:10.1063/1.2710046.","bibtex":"@inproceedings{Dellnitz_Padberg_Post_Thiere_2007, title={Set Oriented Approximation of Invariant Manifolds: Review of Concepts for Astrodynamical Problems}, DOI={10.1063/1.2710046}, booktitle={AIP Conference Proceedings}, author={Dellnitz, Michael and Padberg, Kathrin and Post, Marcus and Thiere, Bianca}, year={2007} }"},"_id":"16561","date_updated":"2022-01-06T06:52:52Z","doi":"10.1063/1.2710046","author":[{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"last_name":"Padberg","first_name":"Kathrin","full_name":"Padberg, Kathrin"},{"last_name":"Post","full_name":"Post, Marcus","first_name":"Marcus"},{"full_name":"Thiere, Bianca","first_name":"Bianca","last_name":"Thiere"}],"publication":"AIP Conference Proceedings","department":[{"_id":"101"}],"status":"public","date_created":"2020-04-15T10:00:16Z","publication_identifier":{"issn":["0094-243X"]},"publication_status":"published","user_id":"15701","title":"Set Oriented Approximation of Invariant Manifolds: Review of Concepts for Astrodynamical Problems"},{"author":[{"last_name":"Schütze","first_name":"Oliver","full_name":"Schütze, Oliver"},{"first_name":"Katrin","full_name":"Witting, Katrin","last_name":"Witting"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"}],"publication":"EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation","department":[{"_id":"101"}],"publication_identifier":{"isbn":["9783642327254","9783642327261"],"issn":["1860-949X","1860-9503"]},"publication_status":"published","status":"public","date_created":"2020-04-16T10:05:59Z","place":"Berlin, Heidelberg","title":"Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems","user_id":"15701","type":"book_chapter","citation":{"chicago":"Schütze, Oliver, Katrin Witting, Sina Ober-Blöbaum, and Michael Dellnitz. “Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems.” In EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation. Berlin, Heidelberg, 2013. https://doi.org/10.1007/978-3-642-32726-1_5.","apa":"Schütze, O., Witting, K., Ober-Blöbaum, S., & Dellnitz, M. (2013). Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems. In EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation. Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32726-1_5","ama":"Schütze O, Witting K, Ober-Blöbaum S, Dellnitz M. Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems. In: EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation. Berlin, Heidelberg; 2013. doi:10.1007/978-3-642-32726-1_5","bibtex":"@inbook{Schütze_Witting_Ober-Blöbaum_Dellnitz_2013, place={Berlin, Heidelberg}, title={Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems}, DOI={10.1007/978-3-642-32726-1_5}, booktitle={EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation}, author={Schütze, Oliver and Witting, Katrin and Ober-Blöbaum, Sina and Dellnitz, Michael}, year={2013} }","mla":"Schütze, Oliver, et al. “Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems.” EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation, 2013, doi:10.1007/978-3-642-32726-1_5.","short":"O. Schütze, K. Witting, S. Ober-Blöbaum, M. Dellnitz, in: EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation, Berlin, Heidelberg, 2013.","ieee":"O. Schütze, K. Witting, S. Ober-Blöbaum, and M. Dellnitz, “Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems,” in EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation, Berlin, Heidelberg, 2013."},"year":"2013","language":[{"iso":"eng"}],"_id":"16670","date_updated":"2022-01-06T06:52:54Z","doi":"10.1007/978-3-642-32726-1_5"},{"title":"Set Oriented Numerical Methods for Dynamical Systems","user_id":"15701","department":[{"_id":"101"}],"publication":"Handbook of Dynamical Systems","author":[{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"last_name":"Junge","first_name":"Oliver","full_name":"Junge, Oliver"}],"publication_identifier":{"isbn":["9780444501684"],"issn":["1874-575X"]},"publication_status":"published","date_created":"2020-04-15T08:37:59Z","status":"public","date_updated":"2022-01-06T06:52:52Z","_id":"16538","doi":"10.1016/s1874-575x(02)80026-1","citation":{"bibtex":"@inbook{Dellnitz_Junge_2002, title={Set Oriented Numerical Methods for Dynamical Systems}, DOI={10.1016/s1874-575x(02)80026-1}, booktitle={Handbook of Dynamical Systems}, author={Dellnitz, Michael and Junge, Oliver}, year={2002} }","mla":"Dellnitz, Michael, and Oliver Junge. “Set Oriented Numerical Methods for Dynamical Systems.” Handbook of Dynamical Systems, 2002, doi:10.1016/s1874-575x(02)80026-1.","chicago":"Dellnitz, Michael, and Oliver Junge. “Set Oriented Numerical Methods for Dynamical Systems.” In Handbook of Dynamical Systems, 2002. https://doi.org/10.1016/s1874-575x(02)80026-1.","ama":"Dellnitz M, Junge O. Set Oriented Numerical Methods for Dynamical Systems. In: Handbook of Dynamical Systems. ; 2002. doi:10.1016/s1874-575x(02)80026-1","apa":"Dellnitz, M., & Junge, O. (2002). Set Oriented Numerical Methods for Dynamical Systems. In Handbook of Dynamical Systems. https://doi.org/10.1016/s1874-575x(02)80026-1","ieee":"M. Dellnitz and O. Junge, “Set Oriented Numerical Methods for Dynamical Systems,” in Handbook of Dynamical Systems, 2002.","short":"M. Dellnitz, O. Junge, in: Handbook of Dynamical Systems, 2002."},"year":"2002","type":"book_chapter","language":[{"iso":"eng"}]},{"doi":"10.1016/s1874-9305(07)80007-0","date_updated":"2022-01-06T06:52:52Z","_id":"16539","language":[{"iso":"eng"}],"year":"2006","type":"book_chapter","citation":{"ieee":"M. Dellnitz and O. Junge, “Set Oriented Numerical Methods in Space Mission Design,” in Elsevier Astrodynamics Series, 2006.","short":"M. Dellnitz, O. Junge, in: Elsevier Astrodynamics Series, 2006.","bibtex":"@inbook{Dellnitz_Junge_2006, title={Set Oriented Numerical Methods in Space Mission Design}, DOI={10.1016/s1874-9305(07)80007-0}, booktitle={Elsevier Astrodynamics Series}, author={Dellnitz, Michael and Junge, Oliver}, year={2006} }","mla":"Dellnitz, Michael, and Oliver Junge. “Set Oriented Numerical Methods in Space Mission Design.” Elsevier Astrodynamics Series, 2006, doi:10.1016/s1874-9305(07)80007-0.","apa":"Dellnitz, M., & Junge, O. (2006). Set Oriented Numerical Methods in Space Mission Design. In Elsevier Astrodynamics Series. https://doi.org/10.1016/s1874-9305(07)80007-0","ama":"Dellnitz M, Junge O. Set Oriented Numerical Methods in Space Mission Design. In: Elsevier Astrodynamics Series. ; 2006. doi:10.1016/s1874-9305(07)80007-0","chicago":"Dellnitz, Michael, and Oliver Junge. “Set Oriented Numerical Methods in Space Mission Design.” In Elsevier Astrodynamics Series, 2006. https://doi.org/10.1016/s1874-9305(07)80007-0."},"user_id":"15701","title":"Set Oriented Numerical Methods in Space Mission Design","status":"public","date_created":"2020-04-15T08:39:13Z","publication_identifier":{"isbn":["9780123735621"],"issn":["1874-9305"]},"publication_status":"published","author":[{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"},{"full_name":"Junge, Oliver","first_name":"Oliver","last_name":"Junge"}],"publication":"Elsevier Astrodynamics Series","department":[{"_id":"101"}]},{"doi":"10.1007/978-3-319-75319-5_3","_id":"8754","date_updated":"2022-01-06T07:04:00Z","language":[{"iso":"eng"}],"page":"47-72","year":"2018","citation":{"chicago":"Beermann, Dennis, Michael Dellnitz, Sebastian Peitz, and Stefan Volkwein. “Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition.” In Reduced-Order Modeling (ROM) for Simulation and Optimization, 47–72. Cham, 2018. https://doi.org/10.1007/978-3-319-75319-5_3.","apa":"Beermann, D., Dellnitz, M., Peitz, S., & Volkwein, S. (2018). Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition. In Reduced-Order Modeling (ROM) for Simulation and Optimization (pp. 47–72). Cham. https://doi.org/10.1007/978-3-319-75319-5_3","ama":"Beermann D, Dellnitz M, Peitz S, Volkwein S. Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition. In: Reduced-Order Modeling (ROM) for Simulation and Optimization. Cham; 2018:47-72. doi:10.1007/978-3-319-75319-5_3","mla":"Beermann, Dennis, et al. “Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition.” Reduced-Order Modeling (ROM) for Simulation and Optimization, 2018, pp. 47–72, doi:10.1007/978-3-319-75319-5_3.","bibtex":"@inbook{Beermann_Dellnitz_Peitz_Volkwein_2018, place={Cham}, title={Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition}, DOI={10.1007/978-3-319-75319-5_3}, booktitle={Reduced-Order Modeling (ROM) for Simulation and Optimization}, author={Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}, year={2018}, pages={47–72} }","short":"D. Beermann, M. Dellnitz, S. Peitz, S. Volkwein, in: Reduced-Order Modeling (ROM) for Simulation and Optimization, Cham, 2018, pp. 47–72.","ieee":"D. Beermann, M. Dellnitz, S. Peitz, and S. Volkwein, “Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition,” in Reduced-Order Modeling (ROM) for Simulation and Optimization, Cham, 2018, pp. 47–72."},"type":"book_chapter","user_id":"47427","title":"Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition","abstract":[{"lang":"eng","text":"In this chapter, we combine a global, derivative-free subdivision algorithm for multiobjective optimization problems with a posteriori error estimates for reduced-order models based on Proper Orthogonal Decomposition in order to efficiently solve multiobjective optimization problems governed by partial differential equations. An error bound for a semilinear heat equation is developed in such a way that the errors in the conflicting objectives can be estimated individually. The resulting algorithm constructs a library of locally valid reduced-order models online using a Greedy (worst-first) search. Using this approach, the number of evaluations of the full-order model can be reduced by a factor of more than 1000."}],"place":"Cham","date_created":"2019-03-29T13:31:20Z","project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"status":"public","publication_identifier":{"isbn":["9783319753188","9783319753195"]},"publication_status":"published","publication":"Reduced-Order Modeling (ROM) for Simulation and Optimization","department":[{"_id":"101"}],"author":[{"last_name":"Beermann","first_name":"Dennis","full_name":"Beermann, Dennis"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"id":"47427","last_name":"Peitz","full_name":"Peitz, Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","first_name":"Sebastian"},{"last_name":"Volkwein","full_name":"Volkwein, Stefan","first_name":"Stefan"}]},{"title":"Solving Optimal Control Problems by Exploiting Inherent Dynamical Systems Structures","user_id":"15701","publication_status":"published","publication_identifier":{"issn":["0938-8974","1432-1467"]},"status":"public","date_created":"2020-04-16T05:53:07Z","author":[{"full_name":"Flaßkamp, Kathrin","first_name":"Kathrin","last_name":"Flaßkamp"},{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"},{"full_name":"Kobilarov, Marin","first_name":"Marin","last_name":"Kobilarov"}],"department":[{"_id":"101"}],"publication":"Journal of Nonlinear Science","doi":"10.1007/s00332-012-9140-7","_id":"16592","date_updated":"2022-01-06T06:52:52Z","type":"journal_article","citation":{"ieee":"K. Flaßkamp, S. Ober-Blöbaum, and M. Kobilarov, “Solving Optimal Control Problems by Exploiting Inherent Dynamical Systems Structures,” Journal of Nonlinear Science, pp. 599–629, 2012.","short":"K. Flaßkamp, S. Ober-Blöbaum, M. Kobilarov, Journal of Nonlinear Science (2012) 599–629.","bibtex":"@article{Flaßkamp_Ober-Blöbaum_Kobilarov_2012, title={Solving Optimal Control Problems by Exploiting Inherent Dynamical Systems Structures}, DOI={10.1007/s00332-012-9140-7}, journal={Journal of Nonlinear Science}, author={Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Kobilarov, Marin}, year={2012}, pages={599–629} }","mla":"Flaßkamp, Kathrin, et al. “Solving Optimal Control Problems by Exploiting Inherent Dynamical Systems Structures.” Journal of Nonlinear Science, 2012, pp. 599–629, doi:10.1007/s00332-012-9140-7.","chicago":"Flaßkamp, Kathrin, Sina Ober-Blöbaum, and Marin Kobilarov. “Solving Optimal Control Problems by Exploiting Inherent Dynamical Systems Structures.” Journal of Nonlinear Science, 2012, 599–629. https://doi.org/10.1007/s00332-012-9140-7.","ama":"Flaßkamp K, Ober-Blöbaum S, Kobilarov M. Solving Optimal Control Problems by Exploiting Inherent Dynamical Systems Structures. Journal of Nonlinear Science. 2012:599-629. doi:10.1007/s00332-012-9140-7","apa":"Flaßkamp, K., Ober-Blöbaum, S., & Kobilarov, M. (2012). Solving Optimal Control Problems by Exploiting Inherent Dynamical Systems Structures. Journal of Nonlinear Science, 599–629. https://doi.org/10.1007/s00332-012-9140-7"},"year":"2012","page":"599-629","language":[{"iso":"eng"}]},{"doi":"10.1002/pamm.201010281","_id":"16590","date_updated":"2022-01-06T06:52:52Z","language":[{"iso":"eng"}],"year":"2010","type":"journal_article","citation":{"bibtex":"@article{Flaßkamp_Ober-Blöbaum_Kobilarov_2010, title={Solving optimal control problems by using inherent dynamical properties}, DOI={10.1002/pamm.201010281}, journal={PAMM}, author={Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Kobilarov, Marin}, year={2010}, pages={577–578} }","mla":"Flaßkamp, Kathrin, et al. “Solving Optimal Control Problems by Using Inherent Dynamical Properties.” PAMM, 2010, pp. 577–78, doi:10.1002/pamm.201010281.","ama":"Flaßkamp K, Ober-Blöbaum S, Kobilarov M. Solving optimal control problems by using inherent dynamical properties. PAMM. 2010:577-578. doi:10.1002/pamm.201010281","apa":"Flaßkamp, K., Ober-Blöbaum, S., & Kobilarov, M. (2010). Solving optimal control problems by using inherent dynamical properties. PAMM, 577–578. https://doi.org/10.1002/pamm.201010281","chicago":"Flaßkamp, Kathrin, Sina Ober-Blöbaum, and Marin Kobilarov. “Solving Optimal Control Problems by Using Inherent Dynamical Properties.” PAMM, 2010, 577–78. https://doi.org/10.1002/pamm.201010281.","ieee":"K. Flaßkamp, S. Ober-Blöbaum, and M. Kobilarov, “Solving optimal control problems by using inherent dynamical properties,” PAMM, pp. 577–578, 2010.","short":"K. Flaßkamp, S. Ober-Blöbaum, M. Kobilarov, PAMM (2010) 577–578."},"page":"577-578","user_id":"15701","title":"Solving optimal control problems by using inherent dynamical properties","status":"public","date_created":"2020-04-16T05:50:45Z","publication_identifier":{"issn":["1617-7061"]},"publication_status":"published","author":[{"last_name":"Flaßkamp","full_name":"Flaßkamp, Kathrin","first_name":"Kathrin"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"},{"full_name":"Kobilarov, Marin","first_name":"Marin","last_name":"Kobilarov"}],"department":[{"_id":"101"}],"publication":"PAMM"},{"publication_identifier":{"issn":["0923-2958","1572-9478"]},"publication_status":"published","date_created":"2020-04-16T10:09:58Z","status":"public","publication":"Celestial Mechanics and Dynamical Astronomy","department":[{"_id":"101"}],"author":[{"full_name":"Tantardini, Marco","first_name":"Marco","last_name":"Tantardini"},{"last_name":"Fantino","full_name":"Fantino, Elena","first_name":"Elena"},{"first_name":"Yuan","full_name":"Ren, Yuan","last_name":"Ren"},{"last_name":"Pergola","full_name":"Pergola, Pierpaolo","first_name":"Pierpaolo"},{"full_name":"Gómez, Gerard","first_name":"Gerard","last_name":"Gómez"},{"last_name":"Masdemont","first_name":"Josep J.","full_name":"Masdemont, Josep J."}],"title":"Spacecraft trajectories to the L3 point of the Sun–Earth three-body problem","user_id":"15701","page":"215-232","year":"2010","citation":{"ama":"Tantardini M, Fantino E, Ren Y, Pergola P, Gómez G, Masdemont JJ. Spacecraft trajectories to the L3 point of the Sun–Earth three-body problem. Celestial Mechanics and Dynamical Astronomy. 2010:215-232. doi:10.1007/s10569-010-9299-x","apa":"Tantardini, M., Fantino, E., Ren, Y., Pergola, P., Gómez, G., & Masdemont, J. J. (2010). Spacecraft trajectories to the L3 point of the Sun–Earth three-body problem. Celestial Mechanics and Dynamical Astronomy, 215–232. https://doi.org/10.1007/s10569-010-9299-x","chicago":"Tantardini, Marco, Elena Fantino, Yuan Ren, Pierpaolo Pergola, Gerard Gómez, and Josep J. Masdemont. “Spacecraft Trajectories to the L3 Point of the Sun–Earth Three-Body Problem.” Celestial Mechanics and Dynamical Astronomy, 2010, 215–32. https://doi.org/10.1007/s10569-010-9299-x.","mla":"Tantardini, Marco, et al. “Spacecraft Trajectories to the L3 Point of the Sun–Earth Three-Body Problem.” Celestial Mechanics and Dynamical Astronomy, 2010, pp. 215–32, doi:10.1007/s10569-010-9299-x.","bibtex":"@article{Tantardini_Fantino_Ren_Pergola_Gómez_Masdemont_2010, title={Spacecraft trajectories to the L3 point of the Sun–Earth three-body problem}, DOI={10.1007/s10569-010-9299-x}, journal={Celestial Mechanics and Dynamical Astronomy}, author={Tantardini, Marco and Fantino, Elena and Ren, Yuan and Pergola, Pierpaolo and Gómez, Gerard and Masdemont, Josep J.}, year={2010}, pages={215–232} }","short":"M. Tantardini, E. Fantino, Y. Ren, P. Pergola, G. Gómez, J.J. Masdemont, Celestial Mechanics and Dynamical Astronomy (2010) 215–232.","ieee":"M. Tantardini, E. Fantino, Y. Ren, P. Pergola, G. Gómez, and J. J. Masdemont, “Spacecraft trajectories to the L3 point of the Sun–Earth three-body problem,” Celestial Mechanics and Dynamical Astronomy, pp. 215–232, 2010."},"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/s10569-010-9299-x","_id":"16673","date_updated":"2022-01-06T06:52:54Z"},{"article_number":"241723","doi":"10.1063/1.5018409","_id":"21942","date_updated":"2022-01-06T06:55:20Z","year":"2018","citation":{"ama":"Boninsegna L, Nüske F, Clementi C. Sparse learning of stochastic dynamical equations. The Journal of Chemical Physics. 2018. doi:10.1063/1.5018409","apa":"Boninsegna, L., Nüske, F., & Clementi, C. (2018). Sparse learning of stochastic dynamical equations. The Journal of Chemical Physics. https://doi.org/10.1063/1.5018409","chicago":"Boninsegna, Lorenzo, Feliks Nüske, and Cecilia Clementi. “Sparse Learning of Stochastic Dynamical Equations.” The Journal of Chemical Physics, 2018. https://doi.org/10.1063/1.5018409.","mla":"Boninsegna, Lorenzo, et al. “Sparse Learning of Stochastic Dynamical Equations.” The Journal of Chemical Physics, 241723, 2018, doi:10.1063/1.5018409.","bibtex":"@article{Boninsegna_Nüske_Clementi_2018, title={Sparse learning of stochastic dynamical equations}, DOI={10.1063/1.5018409}, number={241723}, journal={The Journal of Chemical Physics}, author={Boninsegna, Lorenzo and Nüske, Feliks and Clementi, Cecilia}, year={2018} }","short":"L. Boninsegna, F. Nüske, C. Clementi, The Journal of Chemical Physics (2018).","ieee":"L. Boninsegna, F. Nüske, and C. Clementi, “Sparse learning of stochastic dynamical equations,” The Journal of Chemical Physics, 2018."},"type":"journal_article","language":[{"iso":"eng"}],"title":"Sparse learning of stochastic dynamical equations","user_id":"81513","extern":"1","publication_status":"published","publication_identifier":{"issn":["0021-9606","1089-7690"]},"status":"public","date_created":"2021-04-30T16:59:39Z","author":[{"full_name":"Boninsegna, Lorenzo","first_name":"Lorenzo","last_name":"Boninsegna"},{"first_name":"Feliks","orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks","last_name":"Nüske","id":"81513"},{"full_name":"Clementi, Cecilia","first_name":"Cecilia","last_name":"Clementi"}],"department":[{"_id":"101"}],"publication":"The Journal of Chemical Physics"},{"type":"journal_article","year":"2021","citation":{"ieee":"F. Nüske, P. Koltai, L. Boninsegna, and C. Clementi, “Spectral Properties of Effective Dynamics from Conditional Expectations,” Entropy, 2021.","short":"F. Nüske, P. Koltai, L. Boninsegna, C. Clementi, Entropy (2021).","bibtex":"@article{Nüske_Koltai_Boninsegna_Clementi_2021, title={Spectral Properties of Effective Dynamics from Conditional Expectations}, DOI={10.3390/e23020134}, number={134}, journal={Entropy}, author={Nüske, Feliks and Koltai, Péter and Boninsegna, Lorenzo and Clementi, Cecilia}, year={2021} }","mla":"Nüske, Feliks, et al. “Spectral Properties of Effective Dynamics from Conditional Expectations.” Entropy, 134, 2021, doi:10.3390/e23020134.","ama":"Nüske F, Koltai P, Boninsegna L, Clementi C. Spectral Properties of Effective Dynamics from Conditional Expectations. Entropy. 2021. doi:10.3390/e23020134","apa":"Nüske, F., Koltai, P., Boninsegna, L., & Clementi, C. (2021). Spectral Properties of Effective Dynamics from Conditional Expectations. Entropy. https://doi.org/10.3390/e23020134","chicago":"Nüske, Feliks, Péter Koltai, Lorenzo Boninsegna, and Cecilia Clementi. “Spectral Properties of Effective Dynamics from Conditional Expectations.” Entropy, 2021. https://doi.org/10.3390/e23020134."},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://www.mdpi.com/1099-4300/23/2/134"}],"article_number":"134","doi":"10.3390/e23020134","oa":"1","date_updated":"2022-01-06T06:55:16Z","_id":"21820","publication_status":"published","publication_identifier":{"issn":["1099-4300"]},"status":"public","date_created":"2021-04-28T18:07:56Z","author":[{"last_name":"Nüske","id":"81513","first_name":"Feliks","full_name":"Nüske, Feliks","orcid":"0000-0003-2444-7889"},{"last_name":"Koltai","full_name":"Koltai, Péter","first_name":"Péter"},{"last_name":"Boninsegna","first_name":"Lorenzo","full_name":"Boninsegna, Lorenzo"},{"last_name":"Clementi","full_name":"Clementi, Cecilia","first_name":"Cecilia"}],"publication":"Entropy","department":[{"_id":"101"}],"title":"Spectral Properties of Effective Dynamics from Conditional Expectations","user_id":"81513","abstract":[{"text":"The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the conditioning approach. In this paper, we are interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to the spectrum of the full generator. We prove a new relative error bound in terms of the eigenfunction approximation error for reversible systems. We also present numerical examples indicating that, if Kramers–Moyal (KM) type approximations are used to compute the spectrum of the reduced generator, it seems largely insensitive to the time window used for the KM estimators. We analyze the implications of these observations for systems driven by underdamped Langevin dynamics, and show how meaningful effective dynamics can be defined in this setting.","lang":"eng"}]},{"date_updated":"2022-01-06T06:53:02Z","_id":"17028","type":"report","citation":{"bibtex":"@book{Vasile_Schütze_Junge_Radice_Dellnitz_2007, title={Spiral Trajectories in Global Optimisation of Interplanetary and Orbital Transfers}, publisher={European Space Agency}, author={Vasile, Massimiliano and Schütze, Oliver and Junge, Oliver and Radice, Gimbardo and Dellnitz, Michael}, year={2007} }","mla":"Vasile, Massimiliano, et al. Spiral Trajectories in Global Optimisation of Interplanetary and Orbital Transfers. European Space Agency, 2007.","apa":"Vasile, M., Schütze, O., Junge, O., Radice, G., & Dellnitz, M. (2007). Spiral Trajectories in Global Optimisation of Interplanetary and Orbital Transfers. European Space Agency.","ama":"Vasile M, Schütze O, Junge O, Radice G, Dellnitz M. Spiral Trajectories in Global Optimisation of Interplanetary and Orbital Transfers. European Space Agency; 2007.","chicago":"Vasile, Massimiliano, Oliver Schütze, Oliver Junge, Gimbardo Radice, and Michael Dellnitz. Spiral Trajectories in Global Optimisation of Interplanetary and Orbital Transfers. European Space Agency, 2007.","ieee":"M. Vasile, O. Schütze, O. Junge, G. Radice, and M. Dellnitz, Spiral Trajectories in Global Optimisation of Interplanetary and Orbital Transfers. European Space Agency, 2007.","short":"M. Vasile, O. Schütze, O. Junge, G. Radice, M. Dellnitz, Spiral Trajectories in Global Optimisation of Interplanetary and Orbital Transfers, European Space Agency, 2007."},"year":"2007","report_number":"AO 05/4106","language":[{"iso":"eng"}],"title":"Spiral Trajectories in Global Optimisation of Interplanetary and Orbital Transfers","user_id":"47427","department":[{"_id":"101"}],"publisher":"European Space Agency","author":[{"full_name":"Vasile, Massimiliano","first_name":"Massimiliano","last_name":"Vasile"},{"full_name":"Schütze, Oliver","first_name":"Oliver","last_name":"Schütze"},{"first_name":"Oliver","full_name":"Junge, Oliver","last_name":"Junge"},{"last_name":"Radice","first_name":"Gimbardo","full_name":"Radice, Gimbardo"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"}],"date_created":"2020-05-20T07:30:07Z","status":"public"},{"page":"1487-1501","type":"journal_article","citation":{"apa":"Dellnitz, M., Golubitsky, M., Hohmann, A., & Stewart, I. (1995). Spirals in Scalar Reaction–Diffusion Equations. International Journal of Bifurcation and Chaos, 1487–1501. https://doi.org/10.1142/s0218127495001149","ama":"Dellnitz M, Golubitsky M, Hohmann A, Stewart I. Spirals in Scalar Reaction–Diffusion Equations. International Journal of Bifurcation and Chaos. 1995:1487-1501. doi:10.1142/s0218127495001149","chicago":"Dellnitz, Michael, Martin Golubitsky, Andreas Hohmann, and Ian Stewart. “Spirals in Scalar Reaction–Diffusion Equations.” International Journal of Bifurcation and Chaos, 1995, 1487–1501. https://doi.org/10.1142/s0218127495001149.","bibtex":"@article{Dellnitz_Golubitsky_Hohmann_Stewart_1995, title={Spirals in Scalar Reaction–Diffusion Equations}, DOI={10.1142/s0218127495001149}, journal={International Journal of Bifurcation and Chaos}, author={Dellnitz, Michael and Golubitsky, Martin and Hohmann, Andreas and Stewart, Ian}, year={1995}, pages={1487–1501} }","mla":"Dellnitz, Michael, et al. “Spirals in Scalar Reaction–Diffusion Equations.” International Journal of Bifurcation and Chaos, 1995, pp. 1487–501, doi:10.1142/s0218127495001149.","short":"M. Dellnitz, M. Golubitsky, A. Hohmann, I. Stewart, International Journal of Bifurcation and Chaos (1995) 1487–1501.","ieee":"M. Dellnitz, M. Golubitsky, A. Hohmann, and I. Stewart, “Spirals in Scalar Reaction–Diffusion Equations,” International Journal of Bifurcation and Chaos, pp. 1487–1501, 1995."},"year":"1995","language":[{"iso":"eng"}],"date_updated":"2022-01-06T06:52:52Z","_id":"16551","doi":"10.1142/s0218127495001149","department":[{"_id":"101"}],"publication":"International Journal of Bifurcation and Chaos","author":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"full_name":"Golubitsky, Martin","first_name":"Martin","last_name":"Golubitsky"},{"first_name":"Andreas","full_name":"Hohmann, Andreas","last_name":"Hohmann"},{"last_name":"Stewart","first_name":"Ian","full_name":"Stewart, Ian"}],"publication_status":"published","publication_identifier":{"issn":["0218-1274","1793-6551"]},"date_created":"2020-04-15T09:05:30Z","status":"public","abstract":[{"text":" Spiral patterns have been observed experimentally, numerically, and theoretically in a variety of systems. It is often believed that these spiral wave patterns can occur only in systems of reaction–diffusion equations. We show, both theoretically (using Hopf bifurcation techniques) and numerically (using both direct simulation and continuation of rotating waves) that spiral wave patterns can appear in a single reaction–diffusion equation [ in u(x, t)] on a disk, if one assumes \"spiral\" boundary conditions (ur = muθ). Spiral boundary conditions are motivated by assuming that a solution is infinitesimally an Archimedian spiral near the boundary. It follows from a bifurcation analysis that for this form of spirals there are no singularities in the spiral pattern (technically there is no spiral tip) and that at bifurcation there is a steep gradient between the \"red\" and \"blue\" arms of the spiral. ","lang":"eng"}],"title":"Spirals in Scalar Reaction–Diffusion Equations","user_id":"15701"},{"page":"239-263","citation":{"ieee":"S. Hage-Packhäuser and M. Dellnitz, “Stabilization via symmetry switching in hybrid dynamical systems,” Discrete & Continuous Dynamical Systems - B, vol. 16, no. 1, pp. 239–263, 2011.","short":"S. Hage-Packhäuser, M. Dellnitz, Discrete & Continuous Dynamical Systems - B 16 (2011) 239–263.","bibtex":"@article{Hage-Packhäuser_Dellnitz_2011, title={Stabilization via symmetry switching in hybrid dynamical systems}, volume={16}, DOI={10.3934/dcdsb.2011.16.239}, number={1}, journal={Discrete & Continuous Dynamical Systems - B}, author={Hage-Packhäuser, Sebastian and Dellnitz, Michael}, year={2011}, pages={239–263} }","mla":"Hage-Packhäuser, Sebastian, and Michael Dellnitz. “Stabilization via Symmetry Switching in Hybrid Dynamical Systems.” Discrete & Continuous Dynamical Systems - B, vol. 16, no. 1, 2011, pp. 239–63, doi:10.3934/dcdsb.2011.16.239.","ama":"Hage-Packhäuser S, Dellnitz M. Stabilization via symmetry switching in hybrid dynamical systems. Discrete & Continuous Dynamical Systems - B. 2011;16(1):239-263. doi:10.3934/dcdsb.2011.16.239","apa":"Hage-Packhäuser, S., & Dellnitz, M. (2011). Stabilization via symmetry switching in hybrid dynamical systems. Discrete & Continuous Dynamical Systems - B, 16(1), 239–263. https://doi.org/10.3934/dcdsb.2011.16.239","chicago":"Hage-Packhäuser, Sebastian, and Michael Dellnitz. “Stabilization via Symmetry Switching in Hybrid Dynamical Systems.” Discrete & Continuous Dynamical Systems - B 16, no. 1 (2011): 239–63. https://doi.org/10.3934/dcdsb.2011.16.239."},"type":"journal_article","year":"2011","language":[{"iso":"eng"}],"date_updated":"2022-01-06T06:53:02Z","_id":"17034","intvolume":" 16","doi":"10.3934/dcdsb.2011.16.239","issue":"1","department":[{"_id":"101"}],"publication":"Discrete & Continuous Dynamical Systems - B","author":[{"first_name":"Sebastian","full_name":"Hage-Packhäuser, Sebastian","last_name":"Hage-Packhäuser"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"volume":16,"date_created":"2020-05-20T07:56:34Z","status":"public","title":"Stabilization via symmetry switching in hybrid dynamical systems","user_id":"47427"},{"language":[{"iso":"eng"}],"year":"2012","citation":{"short":"K. Flasskamp, T. Murphey, S. Ober-Blobaum, in: 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012.","ieee":"K. Flasskamp, T. Murphey, and S. Ober-Blobaum, “Switching time optimization in discretized hybrid dynamical systems,” in 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012.","chicago":"Flasskamp, Kathrin, Todd Murphey, and Sina Ober-Blobaum. “Switching Time Optimization in Discretized Hybrid Dynamical Systems.” In 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012. https://doi.org/10.1109/cdc.2012.6426414.","ama":"Flasskamp K, Murphey T, Ober-Blobaum S. Switching time optimization in discretized hybrid dynamical systems. In: 2012 IEEE 51st IEEE Conference on Decision and Control (CDC). ; 2012. doi:10.1109/cdc.2012.6426414","apa":"Flasskamp, K., Murphey, T., & Ober-Blobaum, S. (2012). Switching time optimization in discretized hybrid dynamical systems. In 2012 IEEE 51st IEEE Conference on Decision and Control (CDC). https://doi.org/10.1109/cdc.2012.6426414","bibtex":"@inproceedings{Flasskamp_Murphey_Ober-Blobaum_2012, title={Switching time optimization in discretized hybrid dynamical systems}, DOI={10.1109/cdc.2012.6426414}, booktitle={2012 IEEE 51st IEEE Conference on Decision and Control (CDC)}, author={Flasskamp, Kathrin and Murphey, Todd and Ober-Blobaum, Sina}, year={2012} }","mla":"Flasskamp, Kathrin, et al. “Switching Time Optimization in Discretized Hybrid Dynamical Systems.” 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012, doi:10.1109/cdc.2012.6426414."},"type":"conference","_id":"16591","date_updated":"2022-01-06T06:52:52Z","doi":"10.1109/cdc.2012.6426414","author":[{"last_name":"Flasskamp","full_name":"Flasskamp, Kathrin","first_name":"Kathrin"},{"last_name":"Murphey","first_name":"Todd","full_name":"Murphey, Todd"},{"first_name":"Sina","full_name":"Ober-Blobaum, Sina","last_name":"Ober-Blobaum"}],"department":[{"_id":"101"}],"publication":"2012 IEEE 51st IEEE Conference on Decision and Control (CDC)","status":"public","date_created":"2020-04-16T05:51:38Z","publication_status":"published","publication_identifier":{"isbn":["9781467320665","9781467320658","9781467320634","9781467320641"]},"user_id":"15701","title":"Switching time optimization in discretized hybrid dynamical systems"},{"doi":"10.1088/2632-2153/ac14ad","article_number":"045016","_id":"24170","date_updated":"2022-01-06T06:56:08Z","language":[{"iso":"eng"}],"type":"journal_article","year":"2021","citation":{"mla":"Klus, Stefan, et al. “Symmetric and Antisymmetric Kernels for Machine Learning Problems in Quantum Physics and Chemistry.” Machine Learning: Science and Technology, 045016, 2021, doi:10.1088/2632-2153/ac14ad.","bibtex":"@article{Klus_Gelß_Nüske_Noé_2021, title={Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry}, DOI={10.1088/2632-2153/ac14ad}, number={045016}, journal={Machine Learning: Science and Technology}, author={Klus, Stefan and Gelß, Patrick and Nüske, Feliks and Noé, Frank}, year={2021} }","chicago":"Klus, Stefan, Patrick Gelß, Feliks Nüske, and Frank Noé. “Symmetric and Antisymmetric Kernels for Machine Learning Problems in Quantum Physics and Chemistry.” Machine Learning: Science and Technology, 2021. https://doi.org/10.1088/2632-2153/ac14ad.","apa":"Klus, S., Gelß, P., Nüske, F., & Noé, F. (2021). Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry. Machine Learning: Science and Technology, Article 045016. https://doi.org/10.1088/2632-2153/ac14ad","ama":"Klus S, Gelß P, Nüske F, Noé F. Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry. Machine Learning: Science and Technology. Published online 2021. doi:10.1088/2632-2153/ac14ad","ieee":"S. Klus, P. Gelß, F. Nüske, and F. Noé, “Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry,” Machine Learning: Science and Technology, Art. no. 045016, 2021, doi: 10.1088/2632-2153/ac14ad.","short":"S. Klus, P. Gelß, F. Nüske, F. Noé, Machine Learning: Science and Technology (2021)."},"user_id":"81513","title":"Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry","date_created":"2021-09-12T08:52:57Z","status":"public","publication_status":"published","publication_identifier":{"issn":["2632-2153"]},"publication":"Machine Learning: Science and Technology","department":[{"_id":"101"}],"author":[{"last_name":"Klus","full_name":"Klus, Stefan","first_name":"Stefan"},{"last_name":"Gelß","full_name":"Gelß, Patrick","first_name":"Patrick"},{"id":"81513","last_name":"Nüske","orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks","first_name":"Feliks"},{"last_name":"Noé","first_name":"Frank","full_name":"Noé, Frank"}]},{"doi":"10.3182/20090916-3-es-3003.00013","date_updated":"2022-01-06T06:52:53Z","_id":"16636","page":"68-73","year":"2009","citation":{"short":"A. Meyer, M. Dellnitz, IFAC Proceedings Volumes (2009) 68–73.","ieee":"A. Meyer and M. Dellnitz, “Symmetries in Timed Continuous Petri Nets,” IFAC Proceedings Volumes, pp. 68–73, 2009.","ama":"Meyer A, Dellnitz M. Symmetries in Timed Continuous Petri Nets. IFAC Proceedings Volumes. 2009:68-73. doi:10.3182/20090916-3-es-3003.00013","apa":"Meyer, A., & Dellnitz, M. (2009). Symmetries in Timed Continuous Petri Nets. IFAC Proceedings Volumes, 68–73. https://doi.org/10.3182/20090916-3-es-3003.00013","chicago":"Meyer, A., and M. Dellnitz. “Symmetries in Timed Continuous Petri Nets.” IFAC Proceedings Volumes, 2009, 68–73. https://doi.org/10.3182/20090916-3-es-3003.00013.","bibtex":"@article{Meyer_Dellnitz_2009, title={Symmetries in Timed Continuous Petri Nets}, DOI={10.3182/20090916-3-es-3003.00013}, journal={IFAC Proceedings Volumes}, author={Meyer, A. and Dellnitz, M.}, year={2009}, pages={68–73} }","mla":"Meyer, A., and M. Dellnitz. “Symmetries in Timed Continuous Petri Nets.” IFAC Proceedings Volumes, 2009, pp. 68–73, doi:10.3182/20090916-3-es-3003.00013."},"type":"journal_article","language":[{"iso":"eng"}],"title":"Symmetries in Timed Continuous Petri Nets","user_id":"15701","publication_identifier":{"issn":["1474-6670"]},"publication_status":"published","date_created":"2020-04-16T08:34:44Z","status":"public","publication":"IFAC Proceedings Volumes","department":[{"_id":"101"}],"author":[{"last_name":"Meyer","first_name":"A.","full_name":"Meyer, A."},{"last_name":"Dellnitz","full_name":"Dellnitz, M.","first_name":"M."}]},{"year":"2011","type":"journal_article","citation":{"short":"A. Meyer, M. Dellnitz, M. Hessel-von Molo, Nonlinear Analysis: Hybrid Systems (2011) 125–135.","ieee":"A. Meyer, M. Dellnitz, and M. Hessel-von Molo, “Symmetries in timed continuous Petri nets,” Nonlinear Analysis: Hybrid Systems, pp. 125–135, 2011.","ama":"Meyer A, Dellnitz M, Hessel-von Molo M. Symmetries in timed continuous Petri nets. Nonlinear Analysis: Hybrid Systems. 2011:125-135. doi:10.1016/j.nahs.2010.05.005","apa":"Meyer, A., Dellnitz, M., & Hessel-von Molo, M. (2011). Symmetries in timed continuous Petri nets. Nonlinear Analysis: Hybrid Systems, 125–135. https://doi.org/10.1016/j.nahs.2010.05.005","chicago":"Meyer, A., M. Dellnitz, and M. Hessel-von Molo. “Symmetries in Timed Continuous Petri Nets.” Nonlinear Analysis: Hybrid Systems, 2011, 125–35. https://doi.org/10.1016/j.nahs.2010.05.005.","mla":"Meyer, A., et al. “Symmetries in Timed Continuous Petri Nets.” Nonlinear Analysis: Hybrid Systems, 2011, pp. 125–35, doi:10.1016/j.nahs.2010.05.005.","bibtex":"@article{Meyer_Dellnitz_Hessel-von Molo_2011, title={Symmetries in timed continuous Petri nets}, DOI={10.1016/j.nahs.2010.05.005}, journal={Nonlinear Analysis: Hybrid Systems}, author={Meyer, A. and Dellnitz, M. and Hessel-von Molo, M.}, year={2011}, pages={125–135} }"},"page":"125-135","language":[{"iso":"eng"}],"doi":"10.1016/j.nahs.2010.05.005","date_updated":"2022-01-06T06:52:53Z","_id":"16639","publication_identifier":{"issn":["1751-570X"]},"publication_status":"published","status":"public","date_created":"2020-04-16T08:57:00Z","author":[{"last_name":"Meyer","full_name":"Meyer, A.","first_name":"A."},{"last_name":"Dellnitz","full_name":"Dellnitz, M.","first_name":"M."},{"last_name":"Hessel-von Molo","full_name":"Hessel-von Molo, M.","first_name":"M."}],"department":[{"_id":"101"}],"publication":"Nonlinear Analysis: Hybrid Systems","title":"Symmetries in timed continuous Petri nets","user_id":"15701"},{"publication":"International Journal of Bifurcation and Chaos","department":[{"_id":"101"}],"author":[{"first_name":"Philip J.","full_name":"Aston, Philip J.","last_name":"Aston"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"}],"date_created":"2020-04-15T07:23:50Z","status":"public","publication_identifier":{"issn":["0218-1274","1793-6551"]},"publication_status":"published","abstract":[{"lang":"eng","text":" In an array of coupled oscillators, synchronous chaos may occur in the sense that all the oscillators behave identically although the corresponding motion is chaotic. When a parameter is varied this fully symmetric dynamical state can lose its stability, and the main purpose of this paper is to investigate which type of dynamical behavior is expected to be observed once the loss of stability has occurred. The essential tool is a classification of Lyapunov exponents based on the symmetry of the underlying problem. This classification is crucial in the derivation of the analytical results but it also allows an efficient computation of the dominant Lyapunov exponent associated with each symmetry type. We show how these dominant exponents determine the stability of invariant sets possessing various instantaneous symmetries, and this leads to the idea of symmetry breaking bifurcations of chaotic attractors. Finally, the results and ideas are illustrated for several systems of coupled oscillators. "}],"user_id":"15701","title":"Symmetry Breaking Bifurcations of Chaotic Attractors","language":[{"iso":"eng"}],"page":"1643-1676","year":"1995","citation":{"ama":"Aston PJ, Dellnitz M. Symmetry Breaking Bifurcations of Chaotic Attractors. International Journal of Bifurcation and Chaos. 1995:1643-1676. doi:10.1142/s021812749500123x","apa":"Aston, P. J., & Dellnitz, M. (1995). Symmetry Breaking Bifurcations of Chaotic Attractors. International Journal of Bifurcation and Chaos, 1643–1676. https://doi.org/10.1142/s021812749500123x","chicago":"Aston, Philip J., and Michael Dellnitz. “Symmetry Breaking Bifurcations of Chaotic Attractors.” International Journal of Bifurcation and Chaos, 1995, 1643–76. https://doi.org/10.1142/s021812749500123x.","mla":"Aston, Philip J., and Michael Dellnitz. “Symmetry Breaking Bifurcations of Chaotic Attractors.” International Journal of Bifurcation and Chaos, 1995, pp. 1643–76, doi:10.1142/s021812749500123x.","bibtex":"@article{Aston_Dellnitz_1995, title={Symmetry Breaking Bifurcations of Chaotic Attractors}, DOI={10.1142/s021812749500123x}, journal={International Journal of Bifurcation and Chaos}, author={Aston, Philip J. and Dellnitz, Michael}, year={1995}, pages={1643–1676} }","short":"P.J. Aston, M. Dellnitz, International Journal of Bifurcation and Chaos (1995) 1643–1676.","ieee":"P. J. Aston and M. Dellnitz, “Symmetry Breaking Bifurcations of Chaotic Attractors,” International Journal of Bifurcation and Chaos, pp. 1643–1676, 1995."},"type":"journal_article","_id":"16510","date_updated":"2022-01-06T06:52:52Z","doi":"10.1142/s021812749500123x"},{"author":[{"last_name":"Flasskamp","full_name":"Flasskamp, Kathrin","first_name":"Kathrin"},{"last_name":"Hage-Packhäuser","first_name":"Sebastian","full_name":"Hage-Packhäuser, Sebastian"},{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"}],"publication":"Journal of Computational Dynamics","department":[{"_id":"101"}],"status":"public","date_created":"2020-05-20T08:18:06Z","volume":2,"user_id":"47427","title":"Symmetry exploiting control of hybrid mechanical systems","language":[{"iso":"eng"}],"type":"journal_article","citation":{"apa":"Flasskamp, K., Hage-Packhäuser, S., & Ober-Blöbaum, S. (2015). Symmetry exploiting control of hybrid mechanical systems. Journal of Computational Dynamics, 2(1), 25–50. https://doi.org/10.3934/jcd.2015.2.25","ama":"Flasskamp K, Hage-Packhäuser S, Ober-Blöbaum S. Symmetry exploiting control of hybrid mechanical systems. Journal of Computational Dynamics. 2015;2(1):25-50. doi:10.3934/jcd.2015.2.25","chicago":"Flasskamp, Kathrin, Sebastian Hage-Packhäuser, and Sina Ober-Blöbaum. “Symmetry Exploiting Control of Hybrid Mechanical Systems.” Journal of Computational Dynamics 2, no. 1 (2015): 25–50. https://doi.org/10.3934/jcd.2015.2.25.","mla":"Flasskamp, Kathrin, et al. “Symmetry Exploiting Control of Hybrid Mechanical Systems.” Journal of Computational Dynamics, vol. 2, no. 1, 2015, pp. 25–50, doi:10.3934/jcd.2015.2.25.","bibtex":"@article{Flasskamp_Hage-Packhäuser_Ober-Blöbaum_2015, title={Symmetry exploiting control of hybrid mechanical systems}, volume={2}, DOI={10.3934/jcd.2015.2.25}, number={1}, journal={Journal of Computational Dynamics}, author={Flasskamp, Kathrin and Hage-Packhäuser, Sebastian and Ober-Blöbaum, Sina}, year={2015}, pages={25–50} }","short":"K. Flasskamp, S. Hage-Packhäuser, S. Ober-Blöbaum, Journal of Computational Dynamics 2 (2015) 25–50.","ieee":"K. Flasskamp, S. Hage-Packhäuser, and S. Ober-Blöbaum, “Symmetry exploiting control of hybrid mechanical systems,” Journal of Computational Dynamics, vol. 2, no. 1, pp. 25–50, 2015."},"year":"2015","page":"25-50","_id":"17039","intvolume":" 2","date_updated":"2022-01-06T06:53:03Z","issue":"1","doi":"10.3934/jcd.2015.2.25"},{"language":[{"iso":"eng"}],"citation":{"bibtex":"@inbook{Flaßkamp_Ober-Blöbaum_Peitz_2020, place={Cham}, title={Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach}, DOI={10.1007/978-3-030-51264-4_9}, booktitle={Advances in Dynamics, Optimization and Computation}, publisher={Springer}, author={Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Peitz, Sebastian}, editor={Junge, Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle, KathrinEditors}, year={2020} }","mla":"Flaßkamp, Kathrin, et al. “Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach.” Advances in Dynamics, Optimization and Computation, edited by Oliver Junge et al., Springer, 2020, doi:10.1007/978-3-030-51264-4_9.","chicago":"Flaßkamp, Kathrin, Sina Ober-Blöbaum, and Sebastian Peitz. “Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach.” In Advances in Dynamics, Optimization and Computation, edited by Oliver Junge, Oliver Schütze, Gary Froyland, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle. Cham: Springer, 2020. https://doi.org/10.1007/978-3-030-51264-4_9.","apa":"Flaßkamp, K., Ober-Blöbaum, S., & Peitz, S. (2020). Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach. In O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, & K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation. Cham: Springer. https://doi.org/10.1007/978-3-030-51264-4_9","ama":"Flaßkamp K, Ober-Blöbaum S, Peitz S. Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach. In: Junge O, Schütze O, Froyland G, Ober-Blöbaum S, Padberg-Gehle K, eds. Advances in Dynamics, Optimization and Computation. Cham: Springer; 2020. doi:10.1007/978-3-030-51264-4_9","ieee":"K. Flaßkamp, S. Ober-Blöbaum, and S. Peitz, “Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach,” in Advances in Dynamics, Optimization and Computation, O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, and K. Padberg-Gehle, Eds. Cham: Springer, 2020.","short":"K. Flaßkamp, S. Ober-Blöbaum, S. Peitz, in: O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation, Springer, Cham, 2020."},"year":"2020","type":"book_chapter","date_updated":"2022-01-06T06:53:11Z","_id":"17411","doi":"10.1007/978-3-030-51264-4_9","publisher":"Springer","author":[{"full_name":"Flaßkamp, Kathrin","first_name":"Kathrin","last_name":"Flaßkamp"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"},{"first_name":"Sebastian","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","last_name":"Peitz","id":"47427"}],"publication":"Advances in Dynamics, Optimization and Computation","department":[{"_id":"101"}],"status":"public","date_created":"2020-07-27T09:50:19Z","editor":[{"last_name":"Junge","full_name":"Junge, Oliver","first_name":"Oliver"},{"last_name":"Schütze","full_name":"Schütze, Oliver","first_name":"Oliver"},{"full_name":"Froyland, Gary","first_name":"Gary","last_name":"Froyland"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"},{"last_name":"Padberg-Gehle","full_name":"Padberg-Gehle, Kathrin","first_name":"Kathrin"}],"publication_status":"published","publication_identifier":{"isbn":["9783030512637","9783030512644"],"issn":["2198-4182","2198-4190"]},"place":"Cham","abstract":[{"lang":"eng","text":"Many dynamical systems possess symmetries, e.g. rotational and translational invariances of mechanical systems. These can be beneficially exploited in the design of numerical optimal control methods. We present a model predictive control scheme which is based on a library of precomputed motion primitives. The primitives are equivalence classes w.r.t. the symmetry of the optimal control problems. Trim primitives as relative equilibria w.r.t. this symmetry, play a crucial role in the algorithm. The approach is illustrated using an academic mobile robot example."}],"user_id":"47427","title":"Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach"},{"user_id":"15701","title":"Symmetry of Attractors and the Karhunen-Loève Decomposition","place":"New York, NY","date_created":"2020-04-15T09:02:32Z","status":"public","publication_identifier":{"issn":["0066-5452"],"isbn":["9781461269243","9781461208594"]},"publication_status":"published","publication":"Trends and Perspectives in Applied Mathematics","department":[{"_id":"101"}],"author":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"last_name":"Golubitsky","first_name":"Martin","full_name":"Golubitsky, Martin"},{"last_name":"Nicol","full_name":"Nicol, Matthew","first_name":"Matthew"}],"doi":"10.1007/978-1-4612-0859-4_4","date_updated":"2022-01-06T06:52:52Z","_id":"16549","language":[{"iso":"eng"}],"type":"book_chapter","citation":{"ieee":"M. Dellnitz, M. Golubitsky, and M. Nicol, “Symmetry of Attractors and the Karhunen-Loève Decomposition,” in Trends and Perspectives in Applied Mathematics, New York, NY, 1994.","short":"M. Dellnitz, M. Golubitsky, M. Nicol, in: Trends and Perspectives in Applied Mathematics, New York, NY, 1994.","bibtex":"@inbook{Dellnitz_Golubitsky_Nicol_1994, place={New York, NY}, title={Symmetry of Attractors and the Karhunen-Loève Decomposition}, DOI={10.1007/978-1-4612-0859-4_4}, booktitle={Trends and Perspectives in Applied Mathematics}, author={Dellnitz, Michael and Golubitsky, Martin and Nicol, Matthew}, year={1994} }","mla":"Dellnitz, Michael, et al. “Symmetry of Attractors and the Karhunen-Loève Decomposition.” Trends and Perspectives in Applied Mathematics, 1994, doi:10.1007/978-1-4612-0859-4_4.","apa":"Dellnitz, M., Golubitsky, M., & Nicol, M. (1994). Symmetry of Attractors and the Karhunen-Loève Decomposition. In Trends and Perspectives in Applied Mathematics. New York, NY. https://doi.org/10.1007/978-1-4612-0859-4_4","ama":"Dellnitz M, Golubitsky M, Nicol M. Symmetry of Attractors and the Karhunen-Loève Decomposition. In: Trends and Perspectives in Applied Mathematics. New York, NY; 1994. doi:10.1007/978-1-4612-0859-4_4","chicago":"Dellnitz, Michael, Martin Golubitsky, and Matthew Nicol. “Symmetry of Attractors and the Karhunen-Loève Decomposition.” In Trends and Perspectives in Applied Mathematics. New York, NY, 1994. https://doi.org/10.1007/978-1-4612-0859-4_4."},"year":"1994"},{"title":"Symmetry of attractors and the Perron-Frobenius operator","user_id":"15701","publication_status":"published","publication_identifier":{"issn":["1023-6198","1563-5120"]},"date_created":"2020-04-16T08:30:46Z","status":"public","publication":"Journal of Difference Equations and Applications","department":[{"_id":"101"}],"author":[{"full_name":"Mehta, Prashant G.","first_name":"Prashant G.","last_name":"Mehta"},{"last_name":"Hessel-von Molo","full_name":"Hessel-von Molo, Mirko","first_name":"Mirko"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"doi":"10.1080/10236190601045788","_id":"16632","date_updated":"2022-01-06T06:52:53Z","page":"1147-1178","citation":{"short":"P.G. Mehta, M. Hessel-von Molo, M. Dellnitz, Journal of Difference Equations and Applications (2006) 1147–1178.","ieee":"P. G. Mehta, M. Hessel-von Molo, and M. Dellnitz, “Symmetry of attractors and the Perron-Frobenius operator,” Journal of Difference Equations and Applications, pp. 1147–1178, 2006.","apa":"Mehta, P. G., Hessel-von Molo, M., & Dellnitz, M. (2006). Symmetry of attractors and the Perron-Frobenius operator. Journal of Difference Equations and Applications, 1147–1178. https://doi.org/10.1080/10236190601045788","ama":"Mehta PG, Hessel-von Molo M, Dellnitz M. Symmetry of attractors and the Perron-Frobenius operator. Journal of Difference Equations and Applications. 2006:1147-1178. doi:10.1080/10236190601045788","chicago":"Mehta, Prashant G., Mirko Hessel-von Molo, and Michael Dellnitz. “Symmetry of Attractors and the Perron-Frobenius Operator.” Journal of Difference Equations and Applications, 2006, 1147–78. https://doi.org/10.1080/10236190601045788.","mla":"Mehta, Prashant G., et al. “Symmetry of Attractors and the Perron-Frobenius Operator.” Journal of Difference Equations and Applications, 2006, pp. 1147–78, doi:10.1080/10236190601045788.","bibtex":"@article{Mehta_Hessel-von Molo_Dellnitz_2006, title={Symmetry of attractors and the Perron-Frobenius operator}, DOI={10.1080/10236190601045788}, journal={Journal of Difference Equations and Applications}, author={Mehta, Prashant G. and Hessel-von Molo, Mirko and Dellnitz, Michael}, year={2006}, pages={1147–1178} }"},"type":"journal_article","year":"2006","language":[{"iso":"eng"}]},{"user_id":"15701","title":"Symmetry Reductions in Timed Continuous Petri Nets Under Infinite Server Semantics","author":[{"last_name":"Meyer","full_name":"Meyer, A.","first_name":"A."},{"last_name":"Silva","full_name":"Silva, M.","first_name":"M."}],"publication":"IFAC Proceedings Volumes","department":[{"_id":"101"}],"status":"public","date_created":"2020-04-16T08:52:25Z","publication_identifier":{"issn":["1474-6670"]},"publication_status":"published","_id":"16638","date_updated":"2022-01-06T06:52:53Z","doi":"10.3182/20120606-3-nl-3011.00067","language":[{"iso":"eng"}],"year":"2012","citation":{"mla":"Meyer, A., and M. Silva. “Symmetry Reductions in Timed Continuous Petri Nets Under Infinite Server Semantics.” IFAC Proceedings Volumes, 2012, pp. 153–59, doi:10.3182/20120606-3-nl-3011.00067.","bibtex":"@article{Meyer_Silva_2012, title={Symmetry Reductions in Timed Continuous Petri Nets Under Infinite Server Semantics}, DOI={10.3182/20120606-3-nl-3011.00067}, journal={IFAC Proceedings Volumes}, author={Meyer, A. and Silva, M.}, year={2012}, pages={153–159} }","ama":"Meyer A, Silva M. Symmetry Reductions in Timed Continuous Petri Nets Under Infinite Server Semantics. IFAC Proceedings Volumes. 2012:153-159. doi:10.3182/20120606-3-nl-3011.00067","apa":"Meyer, A., & Silva, M. (2012). Symmetry Reductions in Timed Continuous Petri Nets Under Infinite Server Semantics. IFAC Proceedings Volumes, 153–159. https://doi.org/10.3182/20120606-3-nl-3011.00067","chicago":"Meyer, A., and M. Silva. “Symmetry Reductions in Timed Continuous Petri Nets Under Infinite Server Semantics.” IFAC Proceedings Volumes, 2012, 153–59. https://doi.org/10.3182/20120606-3-nl-3011.00067.","ieee":"A. Meyer and M. Silva, “Symmetry Reductions in Timed Continuous Petri Nets Under Infinite Server Semantics,” IFAC Proceedings Volumes, pp. 153–159, 2012.","short":"A. Meyer, M. Silva, IFAC Proceedings Volumes (2012) 153–159."},"type":"journal_article","page":"153-159"},{"citation":{"apa":"Nüske, F., Gelß, P., Klus, S., & Clementi, C. (2021). Tensor-based computation of metastable and coherent sets. Physica D: Nonlinear Phenomena, Article 133018. https://doi.org/10.1016/j.physd.2021.133018","ama":"Nüske F, Gelß P, Klus S, Clementi C. Tensor-based computation of metastable and coherent sets. Physica D: Nonlinear Phenomena. Published online 2021. doi:10.1016/j.physd.2021.133018","chicago":"Nüske, Feliks, Patrick Gelß, Stefan Klus, and Cecilia Clementi. “Tensor-Based Computation of Metastable and Coherent Sets.” Physica D: Nonlinear Phenomena, 2021. https://doi.org/10.1016/j.physd.2021.133018.","bibtex":"@article{Nüske_Gelß_Klus_Clementi_2021, title={Tensor-based computation of metastable and coherent sets}, DOI={10.1016/j.physd.2021.133018}, number={133018}, journal={Physica D: Nonlinear Phenomena}, author={Nüske, Feliks and Gelß, Patrick and Klus, Stefan and Clementi, Cecilia}, year={2021} }","mla":"Nüske, Feliks, et al. “Tensor-Based Computation of Metastable and Coherent Sets.” Physica D: Nonlinear Phenomena, 133018, 2021, doi:10.1016/j.physd.2021.133018.","short":"F. Nüske, P. Gelß, S. Klus, C. Clementi, Physica D: Nonlinear Phenomena (2021).","ieee":"F. Nüske, P. Gelß, S. Klus, and C. Clementi, “Tensor-based computation of metastable and coherent sets,” Physica D: Nonlinear Phenomena, Art. no. 133018, 2021, doi: 10.1016/j.physd.2021.133018."},"type":"journal_article","year":"2021","language":[{"iso":"eng"}],"date_updated":"2022-01-06T06:56:08Z","_id":"24169","article_number":"133018","doi":"10.1016/j.physd.2021.133018","author":[{"orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks","first_name":"Feliks","id":"81513","last_name":"Nüske"},{"last_name":"Gelß","first_name":"Patrick","full_name":"Gelß, Patrick"},{"last_name":"Klus","first_name":"Stefan","full_name":"Klus, Stefan"},{"last_name":"Clementi","full_name":"Clementi, Cecilia","first_name":"Cecilia"}],"department":[{"_id":"101"}],"publication":"Physica D: Nonlinear Phenomena","publication_status":"published","publication_identifier":{"issn":["0167-2789"]},"status":"public","date_created":"2021-09-12T08:51:24Z","title":"Tensor-based computation of metastable and coherent sets","user_id":"81513"},{"page":"3359-3380","year":"2018","type":"journal_article","citation":{"chicago":"Klus, Stefan, Patrick Gelß, Sebastian Peitz, and Christof Schütte. “Tensor-Based Dynamic Mode Decomposition.” Nonlinearity 31, no. 7 (2018): 3359–80. https://doi.org/10.1088/1361-6544/aabc8f.","ama":"Klus S, Gelß P, Peitz S, Schütte C. Tensor-based dynamic mode decomposition. Nonlinearity. 2018;31(7):3359-3380. doi:10.1088/1361-6544/aabc8f","apa":"Klus, S., Gelß, P., Peitz, S., & Schütte, C. (2018). Tensor-based dynamic mode decomposition. Nonlinearity, 31(7), 3359–3380. https://doi.org/10.1088/1361-6544/aabc8f","bibtex":"@article{Klus_Gelß_Peitz_Schütte_2018, title={Tensor-based dynamic mode decomposition}, volume={31}, DOI={10.1088/1361-6544/aabc8f}, number={7}, journal={Nonlinearity}, author={Klus, Stefan and Gelß, Patrick and Peitz, Sebastian and Schütte, Christof}, year={2018}, pages={3359–3380} }","mla":"Klus, Stefan, et al. “Tensor-Based Dynamic Mode Decomposition.” Nonlinearity, vol. 31, no. 7, 2018, pp. 3359–80, doi:10.1088/1361-6544/aabc8f.","short":"S. Klus, P. Gelß, S. Peitz, C. Schütte, Nonlinearity 31 (2018) 3359–3380.","ieee":"S. Klus, P. Gelß, S. Peitz, and C. Schütte, “Tensor-based dynamic mode decomposition,” Nonlinearity, vol. 31, no. 7, pp. 3359–3380, 2018."},"_id":"8755","intvolume":" 31","issue":"7","publication":"Nonlinearity","author":[{"last_name":"Klus","full_name":"Klus, Stefan","first_name":"Stefan"},{"last_name":"Gelß","full_name":"Gelß, Patrick","first_name":"Patrick"},{"last_name":"Peitz","id":"47427","first_name":"Sebastian","full_name":"Peitz, Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X"},{"first_name":"Christof","full_name":"Schütte, Christof","last_name":"Schütte"}],"volume":31,"date_created":"2019-03-29T13:32:04Z","status":"public","abstract":[{"text":"Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially high-dimensional data sets to compute the corresponding DMD modes and eigenvalues. The goal is to reduce the computational complexity and also the amount of memory required to store the data in order to mitigate the curse of dimensionality. The efficiency of these tensor-based methods will be illustrated with the aid of several different fluid dynamics problems such as the von Kármán vortex street and the simulation of two merging vortices.","lang":"eng"}],"article_type":"original","user_id":"47427","language":[{"iso":"eng"}],"date_updated":"2022-01-06T07:04:00Z","doi":"10.1088/1361-6544/aabc8f","department":[{"_id":"101"}],"publication_identifier":{"issn":["0951-7715","1361-6544"]},"publication_status":"published","project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"title":"Tensor-based dynamic mode decomposition"},{"publication_status":"published","publication_identifier":{"isbn":["9783642625244","9783642565892"]},"date_created":"2020-04-15T09:10:54Z","status":"public","department":[{"_id":"101"}],"publication":"Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems","author":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"last_name":"Froyland","first_name":"Gary","full_name":"Froyland, Gary"},{"first_name":"Oliver","full_name":"Junge, Oliver","last_name":"Junge"}],"title":"The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems","user_id":"15701","place":"Berlin, Heidelberg","type":"book_chapter","year":"2001","citation":{"short":"M. Dellnitz, G. Froyland, O. Junge, in: Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, Berlin, Heidelberg, 2001.","ieee":"M. Dellnitz, G. Froyland, and O. Junge, “The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems,” in Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, Berlin, Heidelberg, 2001.","chicago":"Dellnitz, Michael, Gary Froyland, and Oliver Junge. “The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems.” In Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems. Berlin, Heidelberg, 2001. https://doi.org/10.1007/978-3-642-56589-2_7.","ama":"Dellnitz M, Froyland G, Junge O. The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems. In: Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems. Berlin, Heidelberg; 2001. doi:10.1007/978-3-642-56589-2_7","apa":"Dellnitz, M., Froyland, G., & Junge, O. (2001). The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems. In Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems. Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56589-2_7","bibtex":"@inbook{Dellnitz_Froyland_Junge_2001, place={Berlin, Heidelberg}, title={The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems}, DOI={10.1007/978-3-642-56589-2_7}, booktitle={Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems}, author={Dellnitz, Michael and Froyland, Gary and Junge, Oliver}, year={2001} }","mla":"Dellnitz, Michael, et al. “The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems.” Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, 2001, doi:10.1007/978-3-642-56589-2_7."},"language":[{"iso":"eng"}],"doi":"10.1007/978-3-642-56589-2_7","_id":"16555","date_updated":"2022-01-06T06:52:52Z"},{"date_created":"2020-08-14T15:02:22Z","status":"public","volume":304,"publication":"Advances in Dynamics, Optimization and Computation","author":[{"id":"32655","last_name":"Gerlach","full_name":"Gerlach, Raphael","first_name":"Raphael"},{"first_name":"Adrian","full_name":"Ziessler, Adrian","last_name":"Ziessler"}],"publisher":"Springer International Publishing","user_id":"32655","abstract":[{"text":"In this work we review the novel framework for the computation of finite dimensional invariant sets of infinite dimensional dynamical systems developed in [6] and [36]. By utilizing results on embedding techniques for infinite dimensional systems we extend a classical subdivision scheme [8] as well as a continuation algorithm [7] for the computation of attractors and invariant manifolds of finite dimensional systems to the infinite dimensional case. We show how to implement this approach for the analysis of delay differential equations and partial differential equations and illustrate the feasibility of our implementation by computing the attractor of the Mackey-Glass equation and the unstable manifold of the one-dimensional Kuramoto-Sivashinsky equation.","lang":"eng"}],"page":"66-85","type":"book_chapter","year":"2020","citation":{"mla":"Gerlach, Raphael, and Adrian Ziessler. “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems.” Advances in Dynamics, Optimization and Computation, edited by Oliver Junge et al., vol. 304, Springer International Publishing, 2020, pp. 66–85, doi:10.1007/978-3-030-51264-4_3.","bibtex":"@inbook{Gerlach_Ziessler_2020, place={Cham}, series={Studies in Systems, Decision and Control}, title={The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems}, volume={304}, DOI={10.1007/978-3-030-51264-4_3}, booktitle={Advances in Dynamics, Optimization and Computation}, publisher={Springer International Publishing}, author={Gerlach, Raphael and Ziessler, Adrian}, editor={Junge, Oliver and Schütze, Oliver and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}, year={2020}, pages={66–85}, collection={Studies in Systems, Decision and Control} }","ama":"Gerlach R, Ziessler A. The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems. In: Junge O, Schütze O, Ober-Blöbaum S, Padberg-Gehle K, eds. Advances in Dynamics, Optimization and Computation. Vol 304. Studies in Systems, Decision and Control. Springer International Publishing; 2020:66-85. doi:10.1007/978-3-030-51264-4_3","apa":"Gerlach, R., & Ziessler, A. (2020). The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems. In O. Junge, O. Schütze, S. Ober-Blöbaum, & K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation (Vol. 304, pp. 66–85). Springer International Publishing. https://doi.org/10.1007/978-3-030-51264-4_3","chicago":"Gerlach, Raphael, and Adrian Ziessler. “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems.” In Advances in Dynamics, Optimization and Computation, edited by Oliver Junge, Oliver Schütze, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle, 304:66–85. Studies in Systems, Decision and Control. Cham: Springer International Publishing, 2020. https://doi.org/10.1007/978-3-030-51264-4_3.","ieee":"R. Gerlach and A. Ziessler, “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems,” in Advances in Dynamics, Optimization and Computation, vol. 304, O. Junge, O. Schütze, S. Ober-Blöbaum, and K. Padberg-Gehle, Eds. Cham: Springer International Publishing, 2020, pp. 66–85.","short":"R. Gerlach, A. Ziessler, in: O. Junge, O. Schütze, S. Ober-Blöbaum, K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation, Springer International Publishing, Cham, 2020, pp. 66–85."},"main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/978-3-030-51264-4_3"}],"_id":"17994","intvolume":" 304","publication_status":"published","publication_identifier":{"isbn":["9783030512637","9783030512644"],"issn":["2198-4182","2198-4190"]},"editor":[{"last_name":"Junge","first_name":"Oliver","full_name":"Junge, Oliver"},{"last_name":"Schütze","full_name":"Schütze, Oliver","first_name":"Oliver"},{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"},{"last_name":"Padberg-Gehle","first_name":"Kathrin","full_name":"Padberg-Gehle, Kathrin"}],"department":[{"_id":"101"}],"title":"The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems","place":"Cham","language":[{"iso":"eng"}],"series_title":"Studies in Systems, Decision and Control","doi":"10.1007/978-3-030-51264-4_3","date_updated":"2023-11-17T13:13:25Z"}]