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Guillarmou, Journal of Differential Geometry (to Appear) -- ArXiv:2103.12127 (2024).","bibtex":"@article{Weich_Guedes Bonthonneau_Guillarmou_2024, title={SRB Measures of Anosov Actions}, journal={Journal of Differential Geometry (to appear) -- arXiv:2103.12127}, author={Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin}, year={2024} }","mla":"Weich, Tobias, et al. “SRB Measures of Anosov Actions.” Journal of Differential Geometry (to Appear) -- ArXiv:2103.12127, 2024.","chicago":"Weich, Tobias, Yannick Guedes Bonthonneau, and Colin Guillarmou. “SRB Measures of Anosov Actions.” Journal of Differential Geometry (to Appear) -- ArXiv:2103.12127, 2024.","ama":"Weich T, Guedes Bonthonneau Y, Guillarmou C. SRB Measures of Anosov Actions. Journal of Differential Geometry (to appear) -- arXiv:210312127. Published online 2024.","apa":"Weich, T., Guedes Bonthonneau, Y., & Guillarmou, C. (2024). SRB Measures of Anosov Actions. Journal of Differential Geometry (to Appear) -- ArXiv:2103.12127."},"type":"journal_article","user_id":"49178","ddc":["510"],"title":"SRB Measures of Anosov Actions","external_id":{"arxiv":["https://arxiv.org/abs/2103.12127"]},"has_accepted_license":"1","status":"public","date_created":"2022-06-22T09:56:23Z","file":[{"file_name":"2103.12127.pdf","date_created":"2022-06-22T09:56:08Z","access_level":"open_access","file_size":745870,"file_id":"32098","creator":"weich","date_updated":"2022-06-22T09:56:08Z","content_type":"application/pdf","relation":"main_file"}],"author":[{"last_name":"Weich","id":"49178","first_name":"Tobias","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias"},{"first_name":"Yannick","full_name":"Guedes Bonthonneau, Yannick","last_name":"Guedes Bonthonneau"},{"last_name":"Guillarmou","first_name":"Colin","full_name":"Guillarmou, Colin"}],"file_date_updated":"2022-06-22T09:56:08Z","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"publication":"Journal of Differential Geometry (to appear) -- arXiv:2103.12127"},{"article_number":"013104","issue":"1","_id":"46469","intvolume":" 34","citation":{"mla":"Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational PDEs from Data.” Chaos, vol. 34, no. 1, 013104, AIP Publishing, 2024, doi:10.1063/5.0172287.","bibtex":"@article{Offen_Ober-Blöbaum_2024, title={Learning of discrete models of variational PDEs from data}, volume={34}, DOI={10.1063/5.0172287}, number={1013104}, journal={Chaos}, publisher={AIP Publishing}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2024} }","ama":"Offen C, Ober-Blöbaum S. Learning of discrete models of variational PDEs from data. Chaos. 2024;34(1). doi:10.1063/5.0172287","apa":"Offen, C., & Ober-Blöbaum, S. (2024). Learning of discrete models of variational PDEs from data. Chaos, 34(1), Article 013104. https://doi.org/10.1063/5.0172287","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational PDEs from Data.” Chaos 34, no. 1 (2024). https://doi.org/10.1063/5.0172287.","ieee":"C. Offen and S. Ober-Blöbaum, “Learning of discrete models of variational PDEs from data,” Chaos, vol. 34, no. 1, Art. no. 013104, 2024, doi: 10.1063/5.0172287.","short":"C. Offen, S. Ober-Blöbaum, Chaos 34 (2024)."},"year":"2024","type":"journal_article","ddc":["510"],"user_id":"85279","article_type":"original","abstract":[{"text":"We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train a neural network model of a discrete Lagrangian density such that the discrete Euler--Lagrange equations are consistent with the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian densities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for the training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers guarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical simulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory such as travelling waves. This is possible even when travelling waves are not present in the training data. This is compared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces containing structurally simple solutions when these are not present in the training data. Ideas are demonstrated on examples based on the wave equation and the Schrödinger equation. ","lang":"eng"}],"volume":34,"has_accepted_license":"1","status":"public","date_created":"2023-08-10T08:24:48Z","quality_controlled":"1","publisher":"AIP Publishing","author":[{"first_name":"Christian","full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","id":"85279"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","id":"16494","last_name":"Ober-Blöbaum"}],"file_date_updated":"2024-01-09T11:19:49Z","publication":"Chaos","file":[{"content_type":"application/pdf","date_updated":"2024-01-09T10:48:38Z","relation":"main_file","file_size":13222105,"title":"Accepted Manuscript Chaos","file_id":"50376","creator":"coffen","access_level":"open_access","file_name":"Accepted manuscript with AIP banner CHA23-AR-01370.pdf","date_created":"2024-01-09T10:48:38Z"},{"file_size":12960884,"title":"Learning of discrete models of variational PDEs from data","file_id":"50390","creator":"coffen","date_updated":"2024-01-09T11:19:49Z","content_type":"application/pdf","relation":"main_file","description":"We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train\na neural network model of a discrete Lagrangian density such that the discrete Euler–Lagrange equations are consistent\nwith the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian\ndensities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for\nthe training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers\nguarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical\nsimulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory\nsuch as travelling waves. This is possible even when travelling waves are not present in the training data. This is\ncompared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces\ncontaining structurally simple solutions when these are not present in the training data. Ideas are demonstrated on\nexamples based on the wave equation and the Schrödinger equation.","date_created":"2024-01-09T11:19:49Z","file_name":"LDensityPDE_AIP.pdf","access_level":"open_access"}],"doi":"10.1063/5.0172287","oa":"1","date_updated":"2024-01-09T11:29:06Z","language":[{"iso":"eng"}],"title":"Learning of discrete models of variational PDEs from data","related_material":{"link":[{"url":"https://github.com/Christian-Offen/DLNN_pde","relation":"software","description":"GitHub"}]},"external_id":{"arxiv":["2308.05082 "]},"publication_status":"published","publication_identifier":{"issn":["1054-1500"]},"department":[{"_id":"636"}]},{"_id":"50554","main_file_link":[{"url":"https://www.degruyter.com/document/doi/10.1515/9783110745504/pdf?licenseType=restricted#page=381","open_access":"1"}],"page":"363-372","type":"book_chapter","year":"2024","citation":{"ieee":"S. Prediger and L. Wessel, “31 Sprachbildung im berufsbezogenen Mathematikunterricht.,” in Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis, vol. Band 3, C. Efing and Z. Kalkavan-Aydin, Eds. Berlin: DE GRUYTER, 2024, pp. 363–372.","short":"S. Prediger, L. Wessel, in: C. Efing, Z. Kalkavan-Aydin (Eds.), Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis, DE GRUYTER, Berlin, 2024, pp. 363–372.","bibtex":"@inbook{Prediger_Wessel_2024, place={Berlin}, series={DaZ-Handbücher}, title={31 Sprachbildung im berufsbezogenen Mathematikunterricht.}, volume={Band 3}, booktitle={Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis}, publisher={DE GRUYTER}, author={Prediger, Susanne and Wessel, Lena}, editor={Efing, Christian and Kalkavan-Aydin, Zeynep}, year={2024}, pages={363–372}, collection={DaZ-Handbücher} }","mla":"Prediger, Susanne, and Lena Wessel. “31 Sprachbildung im berufsbezogenen Mathematikunterricht.” Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis, edited by Christian Efing and Zeynep Kalkavan-Aydin, vol. Band 3, DE GRUYTER, 2024, pp. 363–72.","chicago":"Prediger, Susanne, and Lena Wessel. “31 Sprachbildung im berufsbezogenen Mathematikunterricht.” In Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis, edited by Christian Efing and Zeynep Kalkavan-Aydin, Band 3:363–72. DaZ-Handbücher. Berlin: DE GRUYTER, 2024.","apa":"Prediger, S., & Wessel, L. (2024). 31 Sprachbildung im berufsbezogenen Mathematikunterricht. In C. Efing & Z. Kalkavan-Aydin (Eds.), Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis: Vol. Band 3 (pp. 363–372). DE GRUYTER.","ama":"Prediger S, Wessel L. 31 Sprachbildung im berufsbezogenen Mathematikunterricht. In: Efing C, Kalkavan-Aydin Z, eds. Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis. Vol Band 3. DaZ-Handbücher. DE GRUYTER; 2024:363-372."},"user_id":"37888","publication":"Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis","publisher":"DE GRUYTER","author":[{"last_name":"Prediger","first_name":"Susanne","full_name":"Prediger, Susanne"},{"full_name":"Wessel, Lena","first_name":"Lena","id":"85190","last_name":"Wessel"}],"date_created":"2024-01-17T10:58:04Z","status":"public","volume":"Band 3","date_updated":"2024-01-17T11:07:21Z","oa":"1","series_title":"DaZ-Handbücher","language":[{"iso":"ger"}],"place":"Berlin","title":"31 Sprachbildung im berufsbezogenen Mathematikunterricht.","department":[{"_id":"34"},{"_id":"10"},{"_id":"643"}],"publication_identifier":{"isbn":["978-3-11-074544-3"]},"publication_status":"published","editor":[{"first_name":"Christian","full_name":"Efing, Christian","last_name":"Efing"},{"last_name":"Kalkavan-Aydin","first_name":"Zeynep","full_name":"Kalkavan-Aydin, Zeynep"}]},{"status":"public","date_created":"2024-02-07T07:23:23Z","publication_status":"published","publication_identifier":{"issn":["0926-6003","1573-2894"]},"publisher":"Springer Science and Business Media LLC","author":[{"last_name":"Gebken","id":"32643","first_name":"Bennet","full_name":"Gebken, Bennet"}],"publication":"Computational Optimization and Applications","keyword":["Applied Mathematics","Computational Mathematics","Control and Optimization"],"department":[{"_id":"101"}],"user_id":"32643","title":"A note on the convergence of deterministic gradient sampling in nonsmooth optimization","abstract":[{"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.","lang":"eng"}],"language":[{"iso":"eng"}],"citation":{"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.","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","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","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} }","short":"B. Gebken, Computational Optimization and Applications (2024).","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."},"year":"2024","type":"journal_article","doi":"10.1007/s10589-024-00552-0","_id":"51208","date_updated":"2024-02-08T08:05:54Z"},{"status":"public","date_created":"2024-02-06T20:35:36Z","author":[{"last_name":"Lutsko","first_name":"Christopher","full_name":"Lutsko, Christopher"},{"first_name":"Tobias","full_name":"Weich, Tobias","last_name":"Weich"},{"full_name":"Wolf, Lasse Lennart","first_name":"Lasse Lennart","id":"45027","last_name":"Wolf"}],"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"publication":"arXiv:2402.02530","user_id":"49178","title":"Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces","external_id":{"arxiv":["2402.02530"]},"abstract":[{"lang":"eng","text":"Given a real semisimple connected Lie group $G$ and a discrete torsion-free\r\nsubgroup $\\Gamma < G$ we prove a precise connection between growth rates of the\r\ngroup $\\Gamma$, polyhedral bounds on the joint spectrum of the ring of\r\ninvariant differential operators, and the decay of matrix coefficients. In\r\nparticular, this allows us to completely characterize temperedness of\r\n$L^2(\\Gamma\\backslash G)$ in this general setting."}],"language":[{"iso":"eng"}],"year":"2024","citation":{"mla":"Lutsko, Christopher, et al. “Polyhedral Bounds on the Joint Spectrum and Temperedness of Locally Symmetric Spaces.” ArXiv:2402.02530, 2024.","bibtex":"@article{Lutsko_Weich_Wolf_2024, title={Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces}, journal={arXiv:2402.02530}, author={Lutsko, Christopher and Weich, Tobias and Wolf, Lasse Lennart}, year={2024} }","ieee":"C. Lutsko, T. Weich, and L. L. Wolf, “Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces,” arXiv:2402.02530. 2024.","chicago":"Lutsko, Christopher, Tobias Weich, and Lasse Lennart Wolf. “Polyhedral Bounds on the Joint Spectrum and Temperedness of Locally Symmetric Spaces.” ArXiv:2402.02530, 2024.","short":"C. Lutsko, T. Weich, L.L. Wolf, ArXiv:2402.02530 (2024).","ama":"Lutsko C, Weich T, Wolf LL. Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces. arXiv:240202530. Published online 2024.","apa":"Lutsko, C., Weich, T., & Wolf, L. L. (2024). Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces. In arXiv:2402.02530."},"type":"preprint","_id":"51204","date_updated":"2024-02-11T19:56:35Z"},{"intvolume":" 286","_id":"51374","article_number":"110319","issue":"7","year":"2024","type":"journal_article","citation":{"bibtex":"@article{Hasler_Hinrichs_Siebert_2024, title={Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively}, volume={286}, DOI={10.1016/j.jfa.2024.110319}, number={7110319}, journal={Journal of Functional Analysis}, publisher={Elsevier BV}, author={Hasler, David and Hinrichs, Benjamin and Siebert, Oliver}, year={2024} }","mla":"Hasler, David, et al. “Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively.” Journal of Functional Analysis, vol. 286, no. 7, 110319, Elsevier BV, 2024, doi:10.1016/j.jfa.2024.110319.","apa":"Hasler, D., Hinrichs, B., & Siebert, O. (2024). Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively. Journal of Functional Analysis, 286(7), Article 110319. https://doi.org/10.1016/j.jfa.2024.110319","ama":"Hasler D, Hinrichs B, Siebert O. Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively. Journal of Functional Analysis. 2024;286(7). doi:10.1016/j.jfa.2024.110319","chicago":"Hasler, David, Benjamin Hinrichs, and Oliver Siebert. “Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively.” Journal of Functional Analysis 286, no. 7 (2024). https://doi.org/10.1016/j.jfa.2024.110319.","ieee":"D. Hasler, B. Hinrichs, and O. Siebert, “Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively,” Journal of Functional Analysis, vol. 286, no. 7, Art. no. 110319, 2024, doi: 10.1016/j.jfa.2024.110319.","short":"D. Hasler, B. Hinrichs, O. Siebert, Journal of Functional Analysis 286 (2024)."},"extern":"1","user_id":"99427","publication":"Journal of Functional Analysis","keyword":["Analysis"],"publisher":"Elsevier BV","author":[{"full_name":"Hasler, David","first_name":"David","last_name":"Hasler"},{"last_name":"Hinrichs","id":"99427","first_name":"Benjamin","full_name":"Hinrichs, Benjamin","orcid":"0000-0001-9074-1205"},{"full_name":"Siebert, Oliver","first_name":"Oliver","last_name":"Siebert"}],"volume":286,"date_created":"2024-02-18T12:31:28Z","status":"public","date_updated":"2024-02-18T12:32:23Z","doi":"10.1016/j.jfa.2024.110319","language":[{"iso":"eng"}],"external_id":{"arxiv":["2302.06998"]},"title":"Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively","department":[{"_id":"799"}],"publication_identifier":{"issn":["0022-1236"]},"publication_status":"published"},{"user_id":"49063","ddc":["510"],"title":"Ruelle-Taylor resonaces of Anosov actions","has_accepted_license":"1","status":"public","date_created":"2022-06-22T09:56:51Z","publication_status":"published","file":[{"date_created":"2022-06-22T09:56:47Z","file_name":"2007.14275.pdf","access_level":"open_access","file_id":"32102","creator":"weich","file_size":796410,"relation":"main_file","content_type":"application/pdf","date_updated":"2022-06-22T09:56:47Z"}],"author":[{"last_name":"Weich","id":"49178","first_name":"Tobias","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919"},{"last_name":"Guedes Bonthonneau","full_name":"Guedes Bonthonneau, Yannick","first_name":"Yannick"},{"last_name":"Guillarmou","first_name":"Colin","full_name":"Guillarmou, Colin"},{"full_name":"Hilgert, Joachim","first_name":"Joachim","id":"220","last_name":"Hilgert"}],"publication":"J. Europ. Math. Soc.","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}],"file_date_updated":"2022-06-22T09:56:47Z","oa":"1","_id":"32101","date_updated":"2024-02-19T06:25:13Z","language":[{"iso":"eng"}],"type":"journal_article","year":"2024","citation":{"short":"T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, J. Hilgert, J. Europ. Math. Soc. (2024) 1–36.","ieee":"T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, and J. Hilgert, “Ruelle-Taylor resonaces of Anosov actions,” J. Europ. Math. Soc., pp. 1–36, 2024.","chicago":"Weich, Tobias, Yannick Guedes Bonthonneau, Colin Guillarmou, and Joachim Hilgert. “Ruelle-Taylor Resonaces of Anosov Actions.” J. Europ. Math. Soc., 2024, 1–36.","ama":"Weich T, Guedes Bonthonneau Y, Guillarmou C, Hilgert J. Ruelle-Taylor resonaces of Anosov actions. J Europ Math Soc. Published online 2024:1-36.","apa":"Weich, T., Guedes Bonthonneau, Y., Guillarmou, C., & Hilgert, J. (2024). Ruelle-Taylor resonaces of Anosov actions. J. Europ. Math. Soc., 1–36.","bibtex":"@article{Weich_Guedes Bonthonneau_Guillarmou_Hilgert_2024, title={Ruelle-Taylor resonaces of Anosov actions}, journal={J. Europ. Math. Soc.}, author={Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin and Hilgert, Joachim}, year={2024}, pages={1–36} }","mla":"Weich, Tobias, et al. “Ruelle-Taylor Resonaces of Anosov Actions.” J. Europ. Math. Soc., 2024, pp. 1–36."},"page":"1-36"},{"publication_status":"published","date_created":"2024-02-19T10:31:51Z","status":"public","department":[{"_id":"91"}],"author":[{"id":"220","last_name":"Hilgert","full_name":"Hilgert, Joachim","first_name":"Joachim"}],"title":"Quantum-Classical Correspondences for Locally Symmetric Spaces","user_id":"49063","year":"2024","type":"preprint","citation":{"short":"J. Hilgert, (2024).","ieee":"J. Hilgert, “Quantum-Classical Correspondences for Locally Symmetric Spaces.” 2024.","ama":"Hilgert J. Quantum-Classical Correspondences for Locally Symmetric Spaces. Published online 2024.","apa":"Hilgert, J. (2024). Quantum-Classical Correspondences for Locally Symmetric Spaces.","chicago":"Hilgert, Joachim. “Quantum-Classical Correspondences for Locally Symmetric Spaces,” 2024.","mla":"Hilgert, Joachim. Quantum-Classical Correspondences for Locally Symmetric Spaces. 2024.","bibtex":"@article{Hilgert_2024, title={Quantum-Classical Correspondences for Locally Symmetric Spaces}, author={Hilgert, Joachim}, year={2024} }"},"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/pdf/2303.00578.pdf","open_access":"1"}],"oa":"1","date_updated":"2024-02-19T10:32:07Z","_id":"51501"},{"title":"Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems","user_id":"56399","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."}],"publication_status":"published","status":"public","date_created":"2023-07-12T06:35:58Z","publisher":"Springer","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":"Journal of Optimization Theory and Applications","department":[{"_id":"101"},{"_id":"655"}],"doi":"10.1007/s10957-024-02389-3","oa":"1","_id":"46019","date_updated":"2024-02-21T10:13:33Z","citation":{"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.","short":"K. Sonntag, S. Peitz, Journal of Optimization Theory and Applications (2024).","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.","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."},"year":"2024","type":"journal_article","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10957-024-02389-3.pdf","open_access":"1"}]},{"main_file_link":[{"url":"https://arxiv.org/abs/2402.06376","open_access":"1"}],"language":[{"iso":"eng"}],"year":"2024","citation":{"short":"K. Sonntag, B. Gebken, G. Müller, S. Peitz, S. Volkwein, ArXiv:2402.06376 (2024).","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.","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.","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.","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} }"},"type":"preprint","date_updated":"2024-02-21T10:21:03Z","_id":"51334","oa":"1","author":[{"id":"56399","last_name":"Sonntag","orcid":"https://orcid.org/0000-0003-3384-3496","full_name":"Sonntag, Konstantin","first_name":"Konstantin"},{"last_name":"Gebken","id":"32643","first_name":"Bennet","full_name":"Gebken, Bennet"},{"first_name":"Georg","full_name":"Müller, Georg","last_name":"Müller"},{"full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian","id":"47427","last_name":"Peitz"},{"last_name":"Volkwein","full_name":"Volkwein, Stefan","first_name":"Stefan"}],"department":[{"_id":"101"},{"_id":"655"}],"publication":"arXiv:2402.06376","has_accepted_license":"1","status":"public","date_created":"2024-02-13T09:35:26Z","abstract":[{"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.","lang":"eng"}],"external_id":{"arxiv":["\t2402.06376"]},"user_id":"56399","title":"A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces"},{"language":[{"iso":"ger"}],"oa":"1","date_updated":"2024-02-25T21:01:03Z","publication_status":"published","department":[{"_id":"97"},{"_id":"643"}],"title":"Digitalisierung als Chance für alle Prinzipien guten Unterrichts","page":"42 - 47","citation":{"bibtex":"@article{Barzel_Greefrath_Nagel_Hoffmann_2024, title={Digitalisierung als Chance für alle Prinzipien guten Unterrichts}, volume={242}, journal={mathematik lehren}, author={Barzel, Bärbel and Greefrath, Gilbert and Nagel, Mareike and Hoffmann, Max}, year={2024}, pages={42–47} }","mla":"Barzel, Bärbel, et al. “Digitalisierung als Chance für alle Prinzipien guten Unterrichts.” mathematik lehren, vol. 242, 2024, pp. 42–47.","chicago":"Barzel, Bärbel, Gilbert Greefrath, Mareike Nagel, and Max Hoffmann. “Digitalisierung als Chance für alle Prinzipien guten Unterrichts.” mathematik lehren 242 (2024): 42–47.","apa":"Barzel, B., Greefrath, G., Nagel, M., & Hoffmann, M. (2024). Digitalisierung als Chance für alle Prinzipien guten Unterrichts. mathematik lehren, 242, 42–47.","ama":"Barzel B, Greefrath G, Nagel M, Hoffmann M. Digitalisierung als Chance für alle Prinzipien guten Unterrichts. mathematik lehren. 2024;242:42-47.","ieee":"B. Barzel, G. Greefrath, M. Nagel, and M. Hoffmann, “Digitalisierung als Chance für alle Prinzipien guten Unterrichts,” mathematik lehren, vol. 242, pp. 42–47, 2024.","short":"B. Barzel, G. Greefrath, M. Nagel, M. Hoffmann, mathematik lehren 242 (2024) 42–47."},"year":"2024","type":"journal_article","main_file_link":[{"open_access":"1","url":"https://www.friedrich-verlag.de/shop/mwdownloads/download/link/id/114555/"}],"_id":"51841","intvolume":" 242","date_created":"2024-02-25T20:58:51Z","status":"public","has_accepted_license":"1","volume":242,"file":[{"access_level":"closed","date_created":"2024-02-25T20:55:29Z","file_name":"Barzel_etal_2024_DigitalisierungalsChancefrallePrinzipiengut.pdf","relation":"main_file","success":1,"date_updated":"2024-02-25T20:55:29Z","content_type":"application/pdf","creator":"maxh","file_id":"51842","file_size":1410541}],"file_date_updated":"2024-02-25T20:55:29Z","publication":"mathematik lehren","author":[{"last_name":"Barzel","first_name":"Bärbel","full_name":"Barzel, Bärbel"},{"last_name":"Greefrath","full_name":"Greefrath, Gilbert","first_name":"Gilbert"},{"last_name":"Nagel","full_name":"Nagel, Mareike","first_name":"Mareike"},{"last_name":"Hoffmann","id":"32202","first_name":"Max","orcid":"0000-0002-6964-7123","full_name":"Hoffmann, Max"}],"user_id":"32202","ddc":["510","370"],"abstract":[{"text":"athematische Kompetenzen digital zu fördern und digitale Kompetenzen mathematisch zu fördern – dies ist eine Forderung der neuen Bildungsstandards mit Blick auf eine Bildung in der digitalen Welt. Gerade das Potenzial digitaler Medien für das fachliche Lernen wurde in vielen Studien bestätigt. Eine sinnvoll gestaltete Einbettung digitaler Medien bietet die Chance, allen fünf Prinzipien eines guten Unterrichts gerecht zu werden: Verstehensorientierung, Durchgängigkeit, kognitive Aktivierung, Lernendenorientierung & Adaptivität und Kommunikationsförderung. Die flächendeckende Nutzung digitaler Medien etabliert sich bislang nur zögerlich. Aber wie können wir Lehrkräfte stärken, digitale Medien sinnvoll einzusetzen? Wir möchten hier die Bandbreite der Möglichkeiten an Beispielen verdeutlichen, ihren Einsatz motivieren und Wege für einen guten Unterricht aufzeigen.","lang":"ger"}],"article_type":"original"},{"type":"preprint","citation":{"ieee":"C. Dalfó, M. A. Fiol, and E. Steffen, “On token signed graphs,” arXiv:2403.02924. 2024.","short":"C. Dalfó, M.A. Fiol, E. Steffen, ArXiv:2403.02924 (2024).","mla":"Dalfó, C., et al. “On Token Signed Graphs.” ArXiv:2403.02924, 2024.","bibtex":"@article{Dalfó_Fiol_Steffen_2024, title={On token signed graphs}, journal={arXiv:2403.02924}, author={Dalfó, C. and Fiol, M. A. and Steffen, Eckhard}, year={2024} }","chicago":"Dalfó, C., M. A. Fiol, and Eckhard Steffen. “On Token Signed Graphs.” ArXiv:2403.02924, 2024.","apa":"Dalfó, C., Fiol, M. A., & Steffen, E. (2024). On token signed graphs. In arXiv:2403.02924.","ama":"Dalfó C, Fiol MA, Steffen E. On token signed graphs. arXiv:240302924. Published online 2024."},"year":"2024","language":[{"iso":"eng"}],"date_updated":"2024-03-07T08:50:33Z","_id":"52342","department":[{"_id":"542"}],"publication":"arXiv:2403.02924","author":[{"last_name":"Dalfó","full_name":"Dalfó, C.","first_name":"C."},{"first_name":"M. A.","full_name":"Fiol, M. A.","last_name":"Fiol"},{"id":"15548","last_name":"Steffen","full_name":"Steffen, Eckhard","orcid":"0000-0002-9808-7401","first_name":"Eckhard"}],"date_created":"2024-03-07T08:48:39Z","status":"public","external_id":{"arxiv":["2403.02924"]},"abstract":[{"lang":"eng","text":"We introduce the concept of a k-token signed graph and study some of its combinatorial and algebraic properties. We prove that two switching isomorphic signed graphs have switching isomorphic token graphs. Moreover, we show that the Laplacian spectrum of a balanced signed graph is contained in the Laplacian spectra of its k-token signed graph. Besides, we introduce and study the unbalance level of a signed graph, which is a new parameter that measures how far a signed graph is from being balanced. Moreover, we study the relation between the frustration index and the unbalance level of signed graphs and their token signed graphs. "}],"title":"On token signed graphs","user_id":"15540"},{"language":[{"iso":"eng"}],"type":"preprint","year":"2024","citation":{"ieee":"B. Hinrichs and O. Matte, “Feynman-Kac formulas for semigroups generated by multi-polaron Hamiltonians in magnetic fields and on general domains,” arXiv:2403.12147. 2024.","short":"B. Hinrichs, O. Matte, ArXiv:2403.12147 (2024).","mla":"Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formulas for Semigroups Generated by Multi-Polaron Hamiltonians in Magnetic Fields and on General Domains.” ArXiv:2403.12147, 2024.","bibtex":"@article{Hinrichs_Matte_2024, title={Feynman-Kac formulas for semigroups generated by multi-polaron Hamiltonians in magnetic fields and on general domains}, journal={arXiv:2403.12147}, author={Hinrichs, Benjamin and Matte, Oliver}, year={2024} }","chicago":"Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formulas for Semigroups Generated by Multi-Polaron Hamiltonians in Magnetic Fields and on General Domains.” ArXiv:2403.12147, 2024.","ama":"Hinrichs B, Matte O. Feynman-Kac formulas for semigroups generated by multi-polaron Hamiltonians in magnetic fields and on general domains. arXiv:240312147. Published online 2024.","apa":"Hinrichs, B., & Matte, O. (2024). Feynman-Kac formulas for semigroups generated by multi-polaron Hamiltonians in magnetic fields and on general domains. In arXiv:2403.12147."},"date_updated":"2024-03-20T14:56:50Z","_id":"52691","status":"public","date_created":"2024-03-20T14:56:05Z","author":[{"orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin","first_name":"Benjamin","id":"99427","last_name":"Hinrichs"},{"last_name":"Matte","full_name":"Matte, Oliver","first_name":"Oliver"}],"department":[{"_id":"799"}],"publication":"arXiv:2403.12147","user_id":"99427","title":"Feynman-Kac formulas for semigroups generated by multi-polaron Hamiltonians in magnetic fields and on general domains","external_id":{"arxiv":["2403.12147"]},"abstract":[{"lang":"eng","text":"We prove Feynman-Kac formulas for the semigroups generated by selfadjoint\r\noperators in a class containing Fr\\\"ohlich Hamiltonians known from solid state\r\nphysics. The latter model multi-polarons, i.e., a fixed number of quantum\r\nmechanical electrons moving in a polarizable crystal and interacting with the\r\nquantized phonon field generated by the crystal's vibrational modes. Both the\r\nelectrons and phonons can be confined to suitable open subsets of Euclidean\r\nspace. We also include possibly very singular magnetic vector potentials and\r\nelectrostatic potentials. Our Feynman-Kac formulas comprise Fock space\r\noperator-valued multiplicative functionals and can be applied to every vector\r\nin the underlying Hilbert space. In comparison to the renormalized Nelson\r\nmodel, for which analogous Feynman-Kac formulas are known, the analysis of the\r\ncreation and annihilation terms in the multiplicative functionals requires\r\nnovel ideas to overcome difficulties caused by the phonon dispersion relation\r\nbeing constant. Getting these terms under control and generalizing other\r\nconstruction steps so as to cover confined systems are the main achievements of\r\nthis article."}]},{"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."}],"ddc":["510"],"user_id":"97359","publisher":"Oxford University Press (OUP)","author":[{"last_name":"Bick","first_name":"Christian","full_name":"Bick, Christian"},{"orcid":"0000-0002-8054-2058","full_name":"von der Gracht, Sören","first_name":"Sören","id":"97359","last_name":"von der Gracht"}],"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"],"file":[{"file_name":"heteroclinic-dynamics-in-network-dynamical-systems-with-higher-order-interactions.pdf","date_created":"2024-03-22T09:06:07Z","access_level":"closed","file_size":649155,"file_id":"52728","creator":"svdg","date_updated":"2024-03-22T09:06:07Z","content_type":"application/pdf","relation":"main_file","success":1}],"volume":12,"status":"public","has_accepted_license":"1","date_created":"2024-03-22T09:04:57Z","license":"https://creativecommons.org/licenses/by-nc/4.0/","_id":"52726","intvolume":" 12","issue":"2","main_file_link":[{"open_access":"1","url":"https://academic.oup.com/comnet/article-pdf/12/2/cnae009/56832119/cnae009.pdf"}],"year":"2024","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).","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.","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} }","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","external_id":{"arxiv":["2309.02006"]},"title":"Heteroclinic dynamics in network dynamical systems with higher-order interactions","department":[{"_id":"101"}],"publication_identifier":{"issn":["2051-1329"]},"publication_status":"published","date_updated":"2024-03-22T09:11:53Z","doi":"10.1093/comnet/cnae009","oa":"1","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"doi":"10.1007/s00493-023-00078-9","date_updated":"2024-03-22T12:11:35Z","publication_status":"published","publication_identifier":{"issn":["0209-9683","1439-6912"]},"department":[{"_id":"542"}],"title":"Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs","type":"journal_article","citation":{"short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 44 (2024) 429–440.","ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs,” Combinatorica, vol. 44, pp. 429–440, 2024, doi: 10.1007/s00493-023-00078-9.","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs. Combinatorica. 2024;44:429-440. doi:10.1007/s00493-023-00078-9","apa":"Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2024). Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs. Combinatorica, 44, 429–440. https://doi.org/10.1007/s00493-023-00078-9","chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.” Combinatorica 44 (2024): 429–40. https://doi.org/10.1007/s00493-023-00078-9.","mla":"Ma, Yulai, et al. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.” Combinatorica, vol. 44, Springer Science and Business Media LLC, 2024, pp. 429–40, doi:10.1007/s00493-023-00078-9.","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2024, title={Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs}, volume={44}, DOI={10.1007/s00493-023-00078-9}, journal={Combinatorica}, publisher={Springer Science and Business Media LLC}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2024}, pages={429–440} }"},"year":"2024","page":"429-440","_id":"49905","intvolume":" 44","status":"public","date_created":"2023-12-20T10:31:27Z","volume":44,"author":[{"first_name":"Yulai","full_name":"Ma, Yulai","last_name":"Ma","id":"92748"},{"last_name":"Mattiolo","first_name":"Davide","full_name":"Mattiolo, Davide"},{"last_name":"Steffen","id":"15548","first_name":"Eckhard","full_name":"Steffen, Eckhard","orcid":"0000-0002-9808-7401"},{"full_name":"Wolf, Isaak Hieronymus","first_name":"Isaak Hieronymus","id":"88145","last_name":"Wolf"}],"publisher":"Springer Science and Business Media LLC","publication":"Combinatorica","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics"],"user_id":"15540","abstract":[{"lang":"eng","text":"For 0 ≤ t ≤ r let m(t, r) be the maximum number s such that every t-edge-connected r-graph has s pairwise disjoint perfect matchings. There are only a few values of m(t, r) known, for instance m(3, 3) = m(4, r) = 1, and m(t, r) ≤ r − 2 for all t \u0003 = 5,\r\nand m(t, r) ≤ r − 3 if r is even. We prove that m(2l, r) ≤ 3l − 6 for every l ≥ 3 and r ≥ 2l."}]},{"department":[{"_id":"636"}],"publication_status":"published","publication_identifier":{"issn":["2158-2491","2158-2505"]},"title":"A new Lagrangian approach to control affine systems with a quadratic Lagrange term","language":[{"iso":"eng"}],"date_updated":"2024-03-28T16:07:34Z","doi":"10.3934/jcd.2024017","oa":"1","publication":"Journal of Computational Dynamics","keyword":["Optimal control problem","Lagrangian system","Hamiltonian system","Variations","Pontryagin's maximum principle."],"author":[{"last_name":"Leyendecker","first_name":"Sigrid","full_name":"Leyendecker, Sigrid"},{"id":"87909","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya","first_name":"Sofya"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","id":"16494","last_name":"Ober-Blöbaum"},{"full_name":"Almagro, Rodrigo T. Sato Martín de","first_name":"Rodrigo T. Sato Martín de","last_name":"Almagro"},{"first_name":"Flóra Orsolya","full_name":"Szemenyei, Flóra Orsolya","last_name":"Szemenyei"}],"publisher":"American Institute of Mathematical Sciences (AIMS)","volume":"0","date_created":"2024-03-28T15:58:02Z","has_accepted_license":"1","status":"public","abstract":[{"lang":"eng","text":"In this work, we consider optimal control problems for mechanical systems with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an affine control term. Classically, Pontryagin's maximum principle gives necessary optimality conditions for the optimal control problem. For smooth problems, alternatively, a variational approach based on an augmented objective can be followed. Here, we propose a new Lagrangian approach leading to equivalent necessary optimality conditions in the form of Euler-Lagrange equations. Thus, the differential geometric structure (similar to classical Lagrangian dynamics) can be exploited in the framework of optimal control problems. In particular, the formulation enables the symplectic discretisation of the optimal control problem via variational integrators in a straightforward way."}],"article_type":"original","ddc":["510"],"user_id":"87909","main_file_link":[{"open_access":"1","url":"https://www.aimsciences.org/article/doi/10.3934/jcd.2024017"}],"page":"0-0","type":"journal_article","year":"2024","citation":{"apa":"Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., Almagro, R. T. S. M. de, & Szemenyei, F. O. (2024). A new Lagrangian approach to control affine systems with a quadratic Lagrange term. Journal of Computational Dynamics, 0(0), 0–0. https://doi.org/10.3934/jcd.2024017","ama":"Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Almagro RTSM de, Szemenyei FO. A new Lagrangian approach to control affine systems with a quadratic Lagrange term. Journal of Computational Dynamics. 2024;0(0):0-0. doi:10.3934/jcd.2024017","chicago":"Leyendecker, Sigrid, Sofya Maslovskaya, Sina Ober-Blöbaum, Rodrigo T. Sato Martín de Almagro, and Flóra Orsolya Szemenyei. “A New Lagrangian Approach to Control Affine Systems with a Quadratic Lagrange Term.” Journal of Computational Dynamics 0, no. 0 (2024): 0–0. https://doi.org/10.3934/jcd.2024017.","mla":"Leyendecker, Sigrid, et al. “A New Lagrangian Approach to Control Affine Systems with a Quadratic Lagrange Term.” Journal of Computational Dynamics, vol. 0, no. 0, American Institute of Mathematical Sciences (AIMS), 2024, pp. 0–0, doi:10.3934/jcd.2024017.","bibtex":"@article{Leyendecker_Maslovskaya_Ober-Blöbaum_Almagro_Szemenyei_2024, title={A new Lagrangian approach to control affine systems with a quadratic Lagrange term}, volume={0}, DOI={10.3934/jcd.2024017}, number={0}, journal={Journal of Computational Dynamics}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Leyendecker, Sigrid and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Almagro, Rodrigo T. Sato Martín de and Szemenyei, Flóra Orsolya}, year={2024}, pages={0–0} }","short":"S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T.S.M. de Almagro, F.O. Szemenyei, Journal of Computational Dynamics 0 (2024) 0–0.","ieee":"S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R. T. S. M. de Almagro, and F. O. Szemenyei, “A new Lagrangian approach to control affine systems with a quadratic Lagrange term,” Journal of Computational Dynamics, vol. 0, no. 0, pp. 0–0, 2024, doi: 10.3934/jcd.2024017."},"_id":"53101","issue":"0"},{"project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"publication_status":"published","department":[{"_id":"101"},{"_id":"655"}],"title":"On the Universal Transformation of Data-Driven Models to Control Systems","language":[{"iso":"eng"}],"oa":"1","doi":"10.1016/j.automatica.2022.110840","date_updated":"2023-01-07T12:01:58Z","status":"public","date_created":"2021-02-10T07:04:15Z","volume":149,"publisher":"Elsevier","author":[{"orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian","id":"47427","last_name":"Peitz"},{"full_name":"Bieker, Katharina","first_name":"Katharina","id":"32829","last_name":"Bieker"}],"publication":"Automatica","user_id":"47427","abstract":[{"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.","lang":"eng"}],"year":"2023","citation":{"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","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.","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} }","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."},"type":"journal_article","main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/S0005109822007075/pdfft?isDTMRedir=true&download=true"}],"article_number":"110840","_id":"21199","intvolume":" 149"},{"doi":"10.1007/978-3-031-14175-1_9","date_updated":"2023-01-11T08:19:24Z","_id":"35697","page":"181-201","type":"book_chapter","citation":{"short":"L. Ostsieker, R. Biehler, in: Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 2023, pp. 181–201.","ieee":"L. Ostsieker and R. 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