[{"date_updated":"2023-07-04T08:29:22Z","publisher":"Informa UK Limited","author":[{"full_name":"Kirschmer, Markus","id":"82258","last_name":"Kirschmer","first_name":"Markus"},{"first_name":"Gabriele","last_name":"Nebe","full_name":"Nebe, Gabriele"}],"date_created":"2023-07-04T08:28:04Z","volume":31,"title":"Binary Hermitian Lattices over Number Fields","doi":"10.1080/10586458.2019.1618756","publication_status":"published","publication_identifier":{"issn":["1058-6458","1944-950X"]},"issue":"1","year":"2022","citation":{"mla":"Kirschmer, Markus, and Gabriele Nebe. “Binary Hermitian Lattices over Number Fields.” <i>Experimental Mathematics</i>, vol. 31, no. 1, Informa UK Limited, 2022, pp. 280–301, doi:<a href=\"https://doi.org/10.1080/10586458.2019.1618756\">10.1080/10586458.2019.1618756</a>.","short":"M. Kirschmer, G. Nebe, Experimental Mathematics 31 (2022) 280–301.","bibtex":"@article{Kirschmer_Nebe_2022, title={Binary Hermitian Lattices over Number Fields}, volume={31}, DOI={<a href=\"https://doi.org/10.1080/10586458.2019.1618756\">10.1080/10586458.2019.1618756</a>}, number={1}, journal={Experimental Mathematics}, publisher={Informa UK Limited}, author={Kirschmer, Markus and Nebe, Gabriele}, year={2022}, pages={280–301} }","apa":"Kirschmer, M., &#38; Nebe, G. (2022). Binary Hermitian Lattices over Number Fields. <i>Experimental Mathematics</i>, <i>31</i>(1), 280–301. <a href=\"https://doi.org/10.1080/10586458.2019.1618756\">https://doi.org/10.1080/10586458.2019.1618756</a>","ama":"Kirschmer M, Nebe G. Binary Hermitian Lattices over Number Fields. <i>Experimental Mathematics</i>. 2022;31(1):280-301. doi:<a href=\"https://doi.org/10.1080/10586458.2019.1618756\">10.1080/10586458.2019.1618756</a>","chicago":"Kirschmer, Markus, and Gabriele Nebe. “Binary Hermitian Lattices over Number Fields.” <i>Experimental Mathematics</i> 31, no. 1 (2022): 280–301. <a href=\"https://doi.org/10.1080/10586458.2019.1618756\">https://doi.org/10.1080/10586458.2019.1618756</a>.","ieee":"M. Kirschmer and G. Nebe, “Binary Hermitian Lattices over Number Fields,” <i>Experimental Mathematics</i>, vol. 31, no. 1, pp. 280–301, 2022, doi: <a href=\"https://doi.org/10.1080/10586458.2019.1618756\">10.1080/10586458.2019.1618756</a>."},"intvolume":"        31","page":"280-301","_id":"45854","user_id":"93826","department":[{"_id":"102"}],"keyword":["General Mathematics"],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Experimental Mathematics","abstract":[{"text":"In a previous paper the authors developed an algorithm to classify certain quaternary quadratic lattices over totally real fields. The present article applies this algorithm to the classification of binary Hermitian lattices over totally imaginary fields. We use it in particular to classify the 48-dimensional extremal even unimodular lattices over the integers that admit a semilarge automorphism.","lang":"eng"}],"status":"public"},{"publication":"Journal of Geometric Mechanics","abstract":[{"text":"In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby ‘modified’ equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the differential equation has a geometric property then the modified equation may share it. In this way, known properties of differential equations can be applied to the approximation. But for partial differential equations, the known modified equations are of higher order, limiting applicability of the theory. Therefore, we study symmetric solutions of discretized\r\npartial differential equations that arise from a discrete variational principle. These symmetric solutions obey infinite-dimensional functional equations. We show that these equations admit second-order modified equations which are Hamiltonian and also possess first-order Lagrangians in modified coordinates. The modified equation and its associated structures are computed explicitly for the case of rotating travelling waves in the nonlinear wave equation.","lang":"eng"}],"file":[{"relation":"main_file","content_type":"application/pdf","file_id":"31859","file_name":"2_BlendedBEASymmPDE.pdf","access_level":"open_access","title":"Backward error analysis for variational discretisations of PDEs","description":"In backward error analysis, an approximate solution to an equa-\ntion is compared to the exact solution to a nearby ‘modified’ equation. In\nnumerical ordinary differential equations, the two agree up to any power of\nthe step size. If the differential equation has a geometric property then the\nmodified equation may share it. In this way, known properties of differential\nequations can be applied to the approximation. But for partial differential\nequations, the known modified equations are of higher order, limiting appli-\ncability of the theory. Therefore, we study symmetric solutions of discretized\npartial differential equations that arise from a discrete variational principle.\nThese symmetric solutions obey infinite-dimensional functional equations. We\nshow that these equations admit second-order modified equations which are\nHamiltonian and also possess first-order Lagrangians in modified coordinates.\nThe modified equation and its associated structures are computed explicitly\nfor the case of rotating travelling waves in the nonlinear wave equation.","file_size":1507248,"creator":"coffen","date_created":"2022-06-13T09:11:38Z","date_updated":"2022-06-13T09:11:38Z"}],"external_id":{"arxiv":["2006.14172"]},"ddc":["510"],"language":[{"iso":"eng"}],"issue":"3","year":"2022","publisher":"AIMS","date_created":"2020-10-06T16:33:19Z","title":"Backward error analysis for variational discretisations of partial  differential equations","type":"journal_article","status":"public","_id":"19941","department":[{"_id":"636"}],"user_id":"85279","article_type":"original","file_date_updated":"2022-06-13T09:11:38Z","has_accepted_license":"1","publication_status":"published","related_material":{"link":[{"url":"https://github.com/Christian-Offen/multisymplectic","relation":"software"}]},"page":"447 - 471","intvolume":"        14","citation":{"ama":"McLachlan RI, Offen C. Backward error analysis for variational discretisations of partial  differential equations. <i>Journal of Geometric Mechanics</i>. 2022;14(3):447-471. doi:<a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>","ieee":"R. I. McLachlan and C. Offen, “Backward error analysis for variational discretisations of partial  differential equations,” <i>Journal of Geometric Mechanics</i>, vol. 14, no. 3, pp. 447–471, 2022, doi: <a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>.","chicago":"McLachlan, Robert I, and Christian Offen. “Backward Error Analysis for Variational Discretisations of Partial  Differential Equations.” <i>Journal of Geometric Mechanics</i> 14, no. 3 (2022): 447–71. <a href=\"https://doi.org/10.3934/jgm.2022014\">https://doi.org/10.3934/jgm.2022014</a>.","mla":"McLachlan, Robert I., and Christian Offen. “Backward Error Analysis for Variational Discretisations of Partial  Differential Equations.” <i>Journal of Geometric Mechanics</i>, vol. 14, no. 3, AIMS, 2022, pp. 447–71, doi:<a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>.","short":"R.I. McLachlan, C. Offen, Journal of Geometric Mechanics 14 (2022) 447–471.","bibtex":"@article{McLachlan_Offen_2022, title={Backward error analysis for variational discretisations of partial  differential equations}, volume={14}, DOI={<a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>}, number={3}, journal={Journal of Geometric Mechanics}, publisher={AIMS}, author={McLachlan, Robert I and Offen, Christian}, year={2022}, pages={447–471} }","apa":"McLachlan, R. I., &#38; Offen, C. (2022). Backward error analysis for variational discretisations of partial  differential equations. <i>Journal of Geometric Mechanics</i>, <i>14</i>(3), 447–471. <a href=\"https://doi.org/10.3934/jgm.2022014\">https://doi.org/10.3934/jgm.2022014</a>"},"date_updated":"2023-08-10T08:44:55Z","oa":"1","volume":14,"author":[{"first_name":"Robert I","full_name":"McLachlan, Robert I","last_name":"McLachlan"},{"full_name":"Offen, Christian","id":"85279","orcid":"https://orcid.org/0000-0002-5940-8057","last_name":"Offen","first_name":"Christian"}],"doi":"10.3934/jgm.2022014"},{"abstract":[{"text":"Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation laws. To predict Hamiltonian dynamics based on discrete trajectory observations, incorporation of prior knowledge about Hamiltonian structure greatly improves predictions. This is typically done by learning the system's Hamiltonian and then integrating the Hamiltonian vector field with a symplectic integrator. For this, however, Hamiltonian data needs to be approximated based on the trajectory observations. Moreover, the numerical integrator introduces an additional discretisation error. In this paper, we show that an inverse modified Hamiltonian structure adapted to the geometric integrator can be learned directly from observations. A separate approximation step for the Hamiltonian data avoided. The inverse modified data compensates for the discretisation error such that the discretisation error is eliminated. The technique is developed for Gaussian Processes.","lang":"eng"}],"file":[{"relation":"main_file","content_type":"application/pdf","file_name":"SymplecticShadowIntegration_AIP.pdf","access_level":"open_access","file_id":"28734","file_size":2285059,"date_created":"2021-12-13T14:56:15Z","creator":"coffen","date_updated":"2021-12-13T14:56:15Z"}],"publication":"Chaos: An Interdisciplinary Journal of Nonlinear Science","ddc":["510"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["2108.02492"]},"year":"2022","quality_controlled":"1","title":"Symplectic integration of learned Hamiltonian systems","publisher":"AIP","date_created":"2021-08-11T08:24:02Z","status":"public","type":"journal_article","article_type":"original","file_date_updated":"2021-12-13T14:56:15Z","_id":"23382","user_id":"85279","department":[{"_id":"636"}],"citation":{"mla":"Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned Hamiltonian Systems.” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, vol. 32(1), AIP, 2022, doi:<a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>.","bibtex":"@article{Offen_Ober-Blöbaum_2022, title={Symplectic integration of learned Hamiltonian systems}, volume={32(1)}, DOI={<a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2022} }","short":"C. Offen, S. Ober-Blöbaum, Chaos: An Interdisciplinary Journal of Nonlinear Science 32(1) (2022).","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2022). Symplectic integration of learned Hamiltonian systems. <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, <i>32(1)</i>. <a href=\"https://doi.org/10.1063/5.0065913\">https://doi.org/10.1063/5.0065913</a>","ama":"Offen C, Ober-Blöbaum S. Symplectic integration of learned Hamiltonian systems. <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>. 2022;32(1). doi:<a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>","ieee":"C. Offen and S. Ober-Blöbaum, “Symplectic integration of learned Hamiltonian systems,” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, vol. 32(1), 2022, doi: <a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>.","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned Hamiltonian Systems.” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i> 32(1) (2022). <a href=\"https://doi.org/10.1063/5.0065913\">https://doi.org/10.1063/5.0065913</a>."},"publication_status":"published","has_accepted_license":"1","related_material":{"link":[{"relation":"software","description":"GitHub","url":"https://github.com/Christian-Offen/symplectic-shadow-integration"}]},"main_file_link":[{"open_access":"1","url":"https://aip.scitation.org/doi/abs/10.1063/5.0065913"}],"doi":"10.1063/5.0065913","oa":"1","date_updated":"2023-08-10T08:48:14Z","author":[{"last_name":"Offen","orcid":"0000-0002-5940-8057","id":"85279","full_name":"Offen, Christian","first_name":"Christian"},{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494","first_name":"Sina"}],"volume":"32(1)"},{"date_created":"2021-09-12T08:51:24Z","author":[{"first_name":"Feliks","orcid":"0000-0003-2444-7889","last_name":"Nüske","id":"81513","full_name":"Nüske, Feliks"},{"full_name":"Gelß, Patrick","last_name":"Gelß","first_name":"Patrick"},{"last_name":"Klus","full_name":"Klus, Stefan","first_name":"Stefan"},{"first_name":"Cecilia","last_name":"Clementi","full_name":"Clementi, Cecilia"}],"date_updated":"2022-01-06T06:56:08Z","doi":"10.1016/j.physd.2021.133018","title":"Tensor-based computation of metastable and coherent sets","publication_identifier":{"issn":["0167-2789"]},"publication_status":"published","citation":{"chicago":"Nüske, Feliks, Patrick Gelß, Stefan Klus, and Cecilia Clementi. “Tensor-Based Computation of Metastable and Coherent Sets.” <i>Physica D: Nonlinear Phenomena</i>, 2021. <a href=\"https://doi.org/10.1016/j.physd.2021.133018\">https://doi.org/10.1016/j.physd.2021.133018</a>.","ieee":"F. Nüske, P. Gelß, S. Klus, and C. Clementi, “Tensor-based computation of metastable and coherent sets,” <i>Physica D: Nonlinear Phenomena</i>, Art. no. 133018, 2021, doi: <a href=\"https://doi.org/10.1016/j.physd.2021.133018\">10.1016/j.physd.2021.133018</a>.","ama":"Nüske F, Gelß P, Klus S, Clementi C. Tensor-based computation of metastable and coherent sets. <i>Physica D: Nonlinear Phenomena</i>. Published online 2021. doi:<a href=\"https://doi.org/10.1016/j.physd.2021.133018\">10.1016/j.physd.2021.133018</a>","apa":"Nüske, F., Gelß, P., Klus, S., &#38; Clementi, C. (2021). Tensor-based computation of metastable and coherent sets. <i>Physica D: Nonlinear Phenomena</i>, Article 133018. <a href=\"https://doi.org/10.1016/j.physd.2021.133018\">https://doi.org/10.1016/j.physd.2021.133018</a>","short":"F. Nüske, P. Gelß, S. Klus, C. Clementi, Physica D: Nonlinear Phenomena (2021).","bibtex":"@article{Nüske_Gelß_Klus_Clementi_2021, title={Tensor-based computation of metastable and coherent sets}, DOI={<a href=\"https://doi.org/10.1016/j.physd.2021.133018\">10.1016/j.physd.2021.133018</a>}, 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.” <i>Physica D: Nonlinear Phenomena</i>, 133018, 2021, doi:<a href=\"https://doi.org/10.1016/j.physd.2021.133018\">10.1016/j.physd.2021.133018</a>."},"year":"2021","department":[{"_id":"101"}],"user_id":"81513","_id":"24169","language":[{"iso":"eng"}],"article_number":"133018","publication":"Physica D: Nonlinear Phenomena","type":"journal_article","status":"public"},{"publication_status":"published","publication_identifier":{"issn":["2632-2153"]},"citation":{"apa":"Klus, S., Gelß, P., Nüske, F., &#38; Noé, F. (2021). Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry. <i>Machine Learning: Science and Technology</i>, Article 045016. <a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">https://doi.org/10.1088/2632-2153/ac14ad</a>","short":"S. Klus, P. Gelß, F. Nüske, F. Noé, Machine Learning: Science and Technology (2021).","bibtex":"@article{Klus_Gelß_Nüske_Noé_2021, title={Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry}, DOI={<a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">10.1088/2632-2153/ac14ad</a>}, number={045016}, journal={Machine Learning: Science and Technology}, author={Klus, Stefan and Gelß, Patrick and Nüske, Feliks and Noé, Frank}, year={2021} }","mla":"Klus, Stefan, et al. “Symmetric and Antisymmetric Kernels for Machine Learning Problems in Quantum Physics and Chemistry.” <i>Machine Learning: Science and Technology</i>, 045016, 2021, doi:<a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">10.1088/2632-2153/ac14ad</a>.","chicago":"Klus, Stefan, Patrick Gelß, Feliks Nüske, and Frank Noé. “Symmetric and Antisymmetric Kernels for Machine Learning Problems in Quantum Physics and Chemistry.” <i>Machine Learning: Science and Technology</i>, 2021. <a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">https://doi.org/10.1088/2632-2153/ac14ad</a>.","ieee":"S. Klus, P. Gelß, F. Nüske, and F. Noé, “Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry,” <i>Machine Learning: Science and Technology</i>, Art. no. 045016, 2021, doi: <a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">10.1088/2632-2153/ac14ad</a>.","ama":"Klus S, Gelß P, Nüske F, Noé F. Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry. <i>Machine Learning: Science and Technology</i>. Published online 2021. doi:<a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">10.1088/2632-2153/ac14ad</a>"},"year":"2021","date_created":"2021-09-12T08:52:57Z","author":[{"last_name":"Klus","full_name":"Klus, Stefan","first_name":"Stefan"},{"first_name":"Patrick","full_name":"Gelß, Patrick","last_name":"Gelß"},{"first_name":"Feliks","full_name":"Nüske, Feliks","id":"81513","last_name":"Nüske","orcid":"0000-0003-2444-7889"},{"full_name":"Noé, Frank","last_name":"Noé","first_name":"Frank"}],"date_updated":"2022-01-06T06:56:08Z","doi":"10.1088/2632-2153/ac14ad","title":"Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry","type":"journal_article","publication":"Machine Learning: Science and Technology","status":"public","user_id":"81513","department":[{"_id":"101"}],"_id":"24170","language":[{"iso":"eng"}],"article_number":"045016"},{"department":[{"_id":"101"}],"user_id":"32643","_id":"21195","language":[{"iso":"eng"}],"publication":"Cognitive Neurodynamics","type":"journal_article","status":"public","date_created":"2021-02-08T13:16:07Z","author":[{"last_name":"Goelz","full_name":"Goelz, Christian","first_name":"Christian"},{"first_name":"Karin","last_name":"Mora","full_name":"Mora, Karin"},{"full_name":"Stroehlein, Julia Kristin","last_name":"Stroehlein","first_name":"Julia Kristin"},{"last_name":"Haase","full_name":"Haase, Franziska Katharina","first_name":"Franziska Katharina"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"full_name":"Reinsberger, Claus","last_name":"Reinsberger","first_name":"Claus"},{"last_name":"Vieluf","full_name":"Vieluf, Solveig","first_name":"Solveig"}],"date_updated":"2022-01-06T06:54:49Z","doi":"10.1007/s11571-020-09656-9","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s11571-020-09656-9.pdf"}],"title":"Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults","citation":{"ama":"Goelz C, Mora K, Stroehlein JK, et al. Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults. <i>Cognitive Neurodynamics</i>. 2021. doi:<a href=\"https://doi.org/10.1007/s11571-020-09656-9\">10.1007/s11571-020-09656-9</a>","ieee":"C. Goelz <i>et al.</i>, “Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults,” <i>Cognitive Neurodynamics</i>, 2021.","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.” <i>Cognitive Neurodynamics</i>, 2021. <a href=\"https://doi.org/10.1007/s11571-020-09656-9\">https://doi.org/10.1007/s11571-020-09656-9</a>.","bibtex":"@article{Goelz_Mora_Stroehlein_Haase_Dellnitz_Reinsberger_Vieluf_2021, title={Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults}, DOI={<a href=\"https://doi.org/10.1007/s11571-020-09656-9\">10.1007/s11571-020-09656-9</a>}, 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} }","short":"C. Goelz, K. Mora, J.K. Stroehlein, F.K. Haase, M. Dellnitz, C. Reinsberger, S. Vieluf, Cognitive Neurodynamics (2021).","mla":"Goelz, Christian, et al. “Electrophysiological Signatures of Dedifferentiation Differ between Fit and Less Fit Older Adults.” <i>Cognitive Neurodynamics</i>, 2021, doi:<a href=\"https://doi.org/10.1007/s11571-020-09656-9\">10.1007/s11571-020-09656-9</a>.","apa":"Goelz, C., Mora, K., Stroehlein, J. K., Haase, F. K., Dellnitz, M., Reinsberger, C., &#38; Vieluf, S. (2021). Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults. <i>Cognitive Neurodynamics</i>. <a href=\"https://doi.org/10.1007/s11571-020-09656-9\">https://doi.org/10.1007/s11571-020-09656-9</a>"},"year":"2021"},{"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","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."}],"publication":"Mathematical and Computational Applications","title":"Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models","date_created":"2021-03-01T10:46:48Z","year":"2021","issue":"2","article_number":"31","user_id":"47427","department":[{"_id":"101"},{"_id":"655"}],"_id":"21337","status":"public","type":"journal_article","main_file_link":[{"open_access":"1","url":"https://www.mdpi.com/2297-8747/26/2/31/pdf"}],"doi":"10.3390/mca26020031","author":[{"first_name":"Manuel Bastian","full_name":"Berkemeier, Manuel Bastian","id":"51701","last_name":"Berkemeier"},{"first_name":"Sebastian","id":"47427","full_name":"Peitz, Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X"}],"volume":26,"oa":"1","date_updated":"2022-01-06T06:54:55Z","citation":{"ama":"Berkemeier MB, Peitz S. Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models. <i>Mathematical and Computational Applications</i>. 2021;26(2). doi:<a href=\"https://doi.org/10.3390/mca26020031\">10.3390/mca26020031</a>","ieee":"M. B. Berkemeier and S. Peitz, “Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models,” <i>Mathematical and Computational Applications</i>, vol. 26, no. 2, 2021.","chicago":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models.” <i>Mathematical and Computational Applications</i> 26, no. 2 (2021). <a href=\"https://doi.org/10.3390/mca26020031\">https://doi.org/10.3390/mca26020031</a>.","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.” <i>Mathematical and Computational Applications</i>, vol. 26, no. 2, 31, 2021, doi:<a href=\"https://doi.org/10.3390/mca26020031\">10.3390/mca26020031</a>.","bibtex":"@article{Berkemeier_Peitz_2021, title={Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models}, volume={26}, DOI={<a href=\"https://doi.org/10.3390/mca26020031\">10.3390/mca26020031</a>}, number={231}, journal={Mathematical and Computational Applications}, author={Berkemeier, Manuel Bastian and Peitz, Sebastian}, year={2021} }","apa":"Berkemeier, M. B., &#38; Peitz, S. (2021). Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models. <i>Mathematical and Computational Applications</i>, <i>26</i>(2). <a href=\"https://doi.org/10.3390/mca26020031\">https://doi.org/10.3390/mca26020031</a>"},"intvolume":"        26","publication_status":"published","publication_identifier":{"eissn":["2297-8747"]}},{"type":"journal_article","publication":"Entropy","status":"public","abstract":[{"lang":"eng","text":"<jats:p>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.</jats:p>"}],"user_id":"81513","department":[{"_id":"101"}],"_id":"21820","language":[{"iso":"eng"}],"article_number":"134","publication_status":"published","publication_identifier":{"issn":["1099-4300"]},"citation":{"bibtex":"@article{Nüske_Koltai_Boninsegna_Clementi_2021, title={Spectral Properties of Effective Dynamics from Conditional Expectations}, DOI={<a href=\"https://doi.org/10.3390/e23020134\">10.3390/e23020134</a>}, 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.” <i>Entropy</i>, 134, 2021, doi:<a href=\"https://doi.org/10.3390/e23020134\">10.3390/e23020134</a>.","short":"F. Nüske, P. Koltai, L. Boninsegna, C. Clementi, Entropy (2021).","apa":"Nüske, F., Koltai, P., Boninsegna, L., &#38; Clementi, C. (2021). Spectral Properties of Effective Dynamics from Conditional Expectations. <i>Entropy</i>. <a href=\"https://doi.org/10.3390/e23020134\">https://doi.org/10.3390/e23020134</a>","ama":"Nüske F, Koltai P, Boninsegna L, Clementi C. Spectral Properties of Effective Dynamics from Conditional Expectations. <i>Entropy</i>. 2021. doi:<a href=\"https://doi.org/10.3390/e23020134\">10.3390/e23020134</a>","chicago":"Nüske, Feliks, Péter Koltai, Lorenzo Boninsegna, and Cecilia Clementi. “Spectral Properties of Effective Dynamics from Conditional Expectations.” <i>Entropy</i>, 2021. <a href=\"https://doi.org/10.3390/e23020134\">https://doi.org/10.3390/e23020134</a>.","ieee":"F. Nüske, P. Koltai, L. Boninsegna, and C. Clementi, “Spectral Properties of Effective Dynamics from Conditional Expectations,” <i>Entropy</i>, 2021."},"year":"2021","date_created":"2021-04-28T18:07:56Z","author":[{"orcid":"0000-0003-2444-7889","last_name":"Nüske","full_name":"Nüske, Feliks","id":"81513","first_name":"Feliks"},{"full_name":"Koltai, Péter","last_name":"Koltai","first_name":"Péter"},{"first_name":"Lorenzo","full_name":"Boninsegna, Lorenzo","last_name":"Boninsegna"},{"first_name":"Cecilia","full_name":"Clementi, Cecilia","last_name":"Clementi"}],"date_updated":"2022-01-06T06:55:16Z","oa":"1","main_file_link":[{"open_access":"1","url":"https://www.mdpi.com/1099-4300/23/2/134"}],"doi":"10.3390/e23020134","title":"Spectral Properties of Effective Dynamics from Conditional Expectations"},{"date_updated":"2022-01-06T06:52:57Z","oa":"1","date_created":"2020-04-27T09:11:22Z","author":[{"first_name":"Bennet","last_name":"Gebken","full_name":"Gebken, Bennet","id":"32643"},{"last_name":"Peitz","orcid":"0000-0002-3389-793X","id":"47427","full_name":"Peitz, Sebastian","first_name":"Sebastian"}],"volume":188,"title":"An efficient descent method for locally Lipschitz multiobjective optimization problems","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s10957-020-01803-w.pdf"}],"doi":"10.1007/s10957-020-01803-w","publication_status":"published","year":"2021","citation":{"mla":"Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems.” <i>Journal of Optimization Theory and Applications</i>, vol. 188, 2021, pp. 696–723, doi:<a href=\"https://doi.org/10.1007/s10957-020-01803-w\">10.1007/s10957-020-01803-w</a>.","bibtex":"@article{Gebken_Peitz_2021, title={An efficient descent method for locally Lipschitz multiobjective optimization problems}, volume={188}, DOI={<a href=\"https://doi.org/10.1007/s10957-020-01803-w\">10.1007/s10957-020-01803-w</a>}, journal={Journal of Optimization Theory and Applications}, author={Gebken, Bennet and Peitz, Sebastian}, year={2021}, pages={696–723} }","short":"B. Gebken, S. Peitz, Journal of Optimization Theory and Applications 188 (2021) 696–723.","apa":"Gebken, B., &#38; Peitz, S. (2021). An efficient descent method for locally Lipschitz multiobjective optimization problems. <i>Journal of Optimization Theory and Applications</i>, <i>188</i>, 696–723. <a href=\"https://doi.org/10.1007/s10957-020-01803-w\">https://doi.org/10.1007/s10957-020-01803-w</a>","ama":"Gebken B, Peitz S. An efficient descent method for locally Lipschitz multiobjective optimization problems. <i>Journal of Optimization Theory and Applications</i>. 2021;188:696-723. doi:<a href=\"https://doi.org/10.1007/s10957-020-01803-w\">10.1007/s10957-020-01803-w</a>","chicago":"Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems.” <i>Journal of Optimization Theory and Applications</i> 188 (2021): 696–723. <a href=\"https://doi.org/10.1007/s10957-020-01803-w\">https://doi.org/10.1007/s10957-020-01803-w</a>.","ieee":"B. Gebken and S. Peitz, “An efficient descent method for locally Lipschitz multiobjective optimization problems,” <i>Journal of Optimization Theory and Applications</i>, vol. 188, pp. 696–723, 2021."},"intvolume":"       188","page":"696-723","_id":"16867","user_id":"47427","department":[{"_id":"101"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Journal of Optimization Theory and Applications","abstract":[{"lang":"eng","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."}],"status":"public"},{"doi":"10.1007/s10898-020-00983-z","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10898-020-00983-z.pdf","open_access":"1"}],"title":"Inverse multiobjective optimization: Inferring decision criteria from data","volume":80,"date_created":"2020-03-13T12:45:05Z","author":[{"last_name":"Gebken","id":"32643","full_name":"Gebken, Bennet","first_name":"Bennet"},{"first_name":"Sebastian","id":"47427","full_name":"Peitz, Sebastian","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X"}],"oa":"1","date_updated":"2022-01-06T06:52:48Z","publisher":"Springer","page":"3-29","intvolume":"        80","citation":{"ieee":"B. Gebken and S. Peitz, “Inverse multiobjective optimization: Inferring decision criteria from data,” <i>Journal of Global Optimization</i>, vol. 80, pp. 3–29, 2021.","chicago":"Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization: Inferring Decision Criteria from Data.” <i>Journal of Global Optimization</i> 80 (2021): 3–29. <a href=\"https://doi.org/10.1007/s10898-020-00983-z\">https://doi.org/10.1007/s10898-020-00983-z</a>.","ama":"Gebken B, Peitz S. Inverse multiobjective optimization: Inferring decision criteria from data. <i>Journal of Global Optimization</i>. 2021;80:3-29. doi:<a href=\"https://doi.org/10.1007/s10898-020-00983-z\">10.1007/s10898-020-00983-z</a>","bibtex":"@article{Gebken_Peitz_2021, title={Inverse multiobjective optimization: Inferring decision criteria from data}, volume={80}, DOI={<a href=\"https://doi.org/10.1007/s10898-020-00983-z\">10.1007/s10898-020-00983-z</a>}, 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.” <i>Journal of Global Optimization</i>, vol. 80, Springer, 2021, pp. 3–29, doi:<a href=\"https://doi.org/10.1007/s10898-020-00983-z\">10.1007/s10898-020-00983-z</a>.","short":"B. Gebken, S. Peitz, Journal of Global Optimization 80 (2021) 3–29.","apa":"Gebken, B., &#38; Peitz, S. (2021). Inverse multiobjective optimization: Inferring decision criteria from data. <i>Journal of Global Optimization</i>, <i>80</i>, 3–29. <a href=\"https://doi.org/10.1007/s10898-020-00983-z\">https://doi.org/10.1007/s10898-020-00983-z</a>"},"year":"2021","language":[{"iso":"eng"}],"department":[{"_id":"101"}],"user_id":"47427","_id":"16295","status":"public","abstract":[{"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.","lang":"eng"}],"publication":"Journal of Global Optimization","type":"journal_article"},{"year":"2021","citation":{"ama":"Gerlach R. <i>The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems</i>.; 2021. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1278\">10.17619/UNIPB/1-1278</a>","ieee":"R. Gerlach, <i>The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems</i>. 2021.","chicago":"Gerlach, Raphael. <i>The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems</i>, 2021. <a href=\"https://doi.org/10.17619/UNIPB/1-1278\">https://doi.org/10.17619/UNIPB/1-1278</a>.","apa":"Gerlach, R. (2021). <i>The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems</i>. <a href=\"https://doi.org/10.17619/UNIPB/1-1278\">https://doi.org/10.17619/UNIPB/1-1278</a>","mla":"Gerlach, Raphael. <i>The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems</i>. 2021, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1278\">10.17619/UNIPB/1-1278</a>.","short":"R. Gerlach, The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems, 2021.","bibtex":"@book{Gerlach_2021, title={The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-1278\">10.17619/UNIPB/1-1278</a>}, author={Gerlach, Raphael}, year={2021} }"},"date_updated":"2022-06-20T13:40:30Z","oa":"1","date_created":"2022-06-20T09:54:24Z","author":[{"last_name":"Gerlach","full_name":"Gerlach, Raphael","id":"32655","first_name":"Raphael"}],"supervisor":[{"full_name":"Dellnitz , Michael","last_name":"Dellnitz ","first_name":"Michael"},{"first_name":"Péter","full_name":"Koltai, Péter","last_name":"Koltai"}],"title":"The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems","main_file_link":[{"open_access":"1","url":"https://digital.ub.uni-paderborn.de/hs/download/pdf/6214949"}],"doi":"10.17619/UNIPB/1-1278","type":"dissertation","abstract":[{"lang":"ger","text":"Ein zentraler Aspekt bei der Untersuchung dynamischer Systeme ist die Analyse ihrer invarianten Mengen wie des globalen Attraktors und (in)stabiler Mannigfaltigkeiten. Insbesondere wenn das zugrunde liegende System von einem Parameter abhängt, ist es entscheidend, sie im Bezug auf diesen Parameter effizient zu verfolgen. Für die Berechnung invarianter Mengen stützen wir uns für ihre Approximation auf numerische Algorithmen. Typischerweise können diese Methoden jedoch nur auf endlich-dimensionale dynamische Systeme angewendet werden. In dieser Arbeit präsentieren wir daher einen numerischen Rahmen für die globale dynamische Analyse unendlich-dimensionaler Systeme. Wir werden Einbettungstechniken verwenden, um das core dynamical system (CDS) zu definieren, welches ein dynamisch äquivalentes endlich-dimensionales System ist.Das CDS wird dann verwendet, um eingebettete invariante Mengen, also eins-zu-eins Bilder, mittels Mengen-orientierten numerischen Methoden zu approximieren. Bei der Konstruktion des CDS ist es entscheidend, eine geeignete Beobachtungsabbildung auszuwählen und die geeignete inverse Abbildung zu entwerfen. Dazu werden wir geeignete numerische Implementierungen des CDS für DDEs und PDEs vorstellen. Für eine nachfolgende geometrische Analyse der eingebetteten invarianten Menge betrachten wir eine Lerntechnik namens diffusion maps, die ihre intrinsische Geometrie enthüllt sowie ihre Dimension schätzt. Schließlich wenden wir unsere entwickelten numerischen Methoden an einigen bekannten unendlich-dimensionale dynamischen Systeme an, wie die Mackey-Glass-Gleichung, die Kuramoto-Sivashinsky-Gleichung und die Navier-Stokes-Gleichung."},{"lang":"eng","text":"One central aspect in the study of dynamical systems is the analysis of its invariant sets such as the global attractor and (un)stable manifolds. In particular, when the underlying system depends on a parameter it is crucial to efficiently track those set with respect to this parameter. For the computation of invariant sets we rely on numerical algorithms for their approximation but typically those tools can only be applied to finite-dimensional dynamical systems. Thus, in thesis we present a numerical framework for the global dynamical analysis of infinite-dimensional systems. We will use embedding techniques for the definition of the core dynamical system (CDS) which is a dynamically equivalent finite-dimensional system. The CDS is then used for the approximation of related embedded invariant sets, i.e, one-to-one images, by set-oriented numerical methods. For the construction of the CDS it is crucial to choose an appropriate observation map and to design its corresponding inverse. Therefore, we will present suitable numerical realizations of the CDS for DDEs and PDEs. For a subsequent geometric analysis of the embedded invariant set we will consider a manifold learning technique called diffusion maps which reveals its intrinsic geometry and estimates its dimension. Finally, we apply our develop numerical tools on some well-known infinite-dimensional dynamical systems such as the Mackey-Glass equation, the Kuramoto-Sivashinsky equation and the Navier-Stokes equation."}],"status":"public","_id":"32057","user_id":"32643","department":[{"_id":"101"}],"language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Theoretical Computer Science"],"user_id":"15540","department":[{"_id":"542"}],"_id":"34042","status":"public","type":"journal_article","publication":"Journal of Combinatorial Theory, Series B","doi":"10.1016/j.jctb.2021.11.001","title":"Nowhere-zero 3-flows in toroidal graphs","date_created":"2022-11-09T08:43:55Z","author":[{"last_name":"Li","full_name":"Li, Jiaao","first_name":"Jiaao"},{"first_name":"Yulai","last_name":"Ma","id":"92748","full_name":"Ma, Yulai"},{"first_name":"Zhengke","last_name":"Miao","full_name":"Miao, Zhengke"},{"full_name":"Shi, Yongtang","last_name":"Shi","first_name":"Yongtang"},{"first_name":"Weifan","last_name":"Wang","full_name":"Wang, Weifan"},{"last_name":"Zhang","full_name":"Zhang, Cun-Quan","first_name":"Cun-Quan"}],"volume":153,"publisher":"Elsevier BV","date_updated":"2022-11-09T08:44:37Z","citation":{"ieee":"J. Li, Y. Ma, Z. Miao, Y. Shi, W. Wang, and C.-Q. Zhang, “Nowhere-zero 3-flows in toroidal graphs,” <i>Journal of Combinatorial Theory, Series B</i>, vol. 153, pp. 61–80, 2021, doi: <a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">10.1016/j.jctb.2021.11.001</a>.","chicago":"Li, Jiaao, Yulai Ma, Zhengke Miao, Yongtang Shi, Weifan Wang, and Cun-Quan Zhang. “Nowhere-Zero 3-Flows in Toroidal Graphs.” <i>Journal of Combinatorial Theory, Series B</i> 153 (2021): 61–80. <a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">https://doi.org/10.1016/j.jctb.2021.11.001</a>.","apa":"Li, J., Ma, Y., Miao, Z., Shi, Y., Wang, W., &#38; Zhang, C.-Q. (2021). Nowhere-zero 3-flows in toroidal graphs. <i>Journal of Combinatorial Theory, Series B</i>, <i>153</i>, 61–80. <a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">https://doi.org/10.1016/j.jctb.2021.11.001</a>","ama":"Li J, Ma Y, Miao Z, Shi Y, Wang W, Zhang C-Q. Nowhere-zero 3-flows in toroidal graphs. <i>Journal of Combinatorial Theory, Series B</i>. 2021;153:61-80. doi:<a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">10.1016/j.jctb.2021.11.001</a>","mla":"Li, Jiaao, et al. “Nowhere-Zero 3-Flows in Toroidal Graphs.” <i>Journal of Combinatorial Theory, Series B</i>, vol. 153, Elsevier BV, 2021, pp. 61–80, doi:<a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">10.1016/j.jctb.2021.11.001</a>.","bibtex":"@article{Li_Ma_Miao_Shi_Wang_Zhang_2021, title={Nowhere-zero 3-flows in toroidal graphs}, volume={153}, DOI={<a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">10.1016/j.jctb.2021.11.001</a>}, journal={Journal of Combinatorial Theory, Series B}, publisher={Elsevier BV}, author={Li, Jiaao and Ma, Yulai and Miao, Zhengke and Shi, Yongtang and Wang, Weifan and Zhang, Cun-Quan}, year={2021}, pages={61–80} }","short":"J. Li, Y. Ma, Z. Miao, Y. Shi, W. Wang, C.-Q. Zhang, Journal of Combinatorial Theory, Series B 153 (2021) 61–80."},"page":"61-80","intvolume":"       153","year":"2021","publication_status":"published","publication_identifier":{"issn":["0095-8956"]}},{"status":"public","type":"conference","publication":"7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC","language":[{"iso":"eng"}],"_id":"29421","user_id":"15694","department":[{"_id":"636"}],"year":"2021","citation":{"chicago":"Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational Integrators.” In <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>, edited by IFAC-PapersOnLine, 54(19):327–33, 2021.","ieee":"S. Ober-Blöbaum and M. Vermeeren, “Superconvergence of galerkin variational integrators,” in <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>, 2021, vol. 54(19), pp. 327–333.","ama":"Ober-Blöbaum S, Vermeeren M. Superconvergence of galerkin variational integrators. In: IFAC-PapersOnLine, ed. <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>. Vol 54(19). ; 2021:327-333.","apa":"Ober-Blöbaum, S., &#38; Vermeeren, M. (2021). Superconvergence of galerkin variational integrators. In IFAC-PapersOnLine (Ed.), <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC: Vol. 54(19)</i> (pp. 327–333).","short":"S. Ober-Blöbaum, M. Vermeeren, in: IFAC-PapersOnLine (Ed.), 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC, 2021, pp. 327–333.","bibtex":"@inproceedings{Ober-Blöbaum_Vermeeren_2021, title={Superconvergence of galerkin variational integrators}, volume={54(19)}, booktitle={7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC}, author={Ober-Blöbaum, Sina and Vermeeren, M.}, editor={IFAC-PapersOnLine}, year={2021}, pages={327–333} }","mla":"Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational Integrators.” <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>, edited by IFAC-PapersOnLine, vol. 54(19), 2021, pp. 327–33."},"corporate_editor":["IFAC-PapersOnLine"],"page":"327-333","title":"Superconvergence of galerkin variational integrators","date_updated":"2022-01-21T13:36:53Z","date_created":"2022-01-18T14:27:56Z","author":[{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"},{"first_name":"M.","last_name":"Vermeeren","full_name":"Vermeeren, M."}],"volume":"54(19)"},{"department":[{"_id":"101"}],"user_id":"15694","_id":"16294","project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"language":[{"iso":"eng"}],"publication":"International Journal of Robust and Nonlinear Control","type":"journal_article","status":"public","abstract":[{"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.","lang":"eng"}],"volume":"31(2)","author":[{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"},{"id":"47427","full_name":"Peitz, Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian"}],"date_created":"2020-03-13T12:44:36Z","oa":"1","date_updated":"2022-01-24T13:27:50Z","doi":"10.1002/rnc.5281","main_file_link":[{"open_access":"1","url":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/rnc.5281"}],"title":"Explicit multiobjective model predictive control for nonlinear systems  with symmetries","page":"380-403","citation":{"ama":"Ober-Blöbaum S, Peitz S. Explicit multiobjective model predictive control for nonlinear systems  with symmetries. <i>International Journal of Robust and Nonlinear Control</i>. 2021;31(2):380-403. doi:<a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>","chicago":"Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems  with Symmetries.” <i>International Journal of Robust and Nonlinear Control</i> 31(2) (2021): 380–403. <a href=\"https://doi.org/10.1002/rnc.5281\">https://doi.org/10.1002/rnc.5281</a>.","ieee":"S. Ober-Blöbaum and S. Peitz, “Explicit multiobjective model predictive control for nonlinear systems  with symmetries,” <i>International Journal of Robust and Nonlinear Control</i>, vol. 31(2), pp. 380–403, 2021, doi: <a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>.","mla":"Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems  with Symmetries.” <i>International Journal of Robust and Nonlinear Control</i>, vol. 31(2), 2021, pp. 380–403, doi:<a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>.","bibtex":"@article{Ober-Blöbaum_Peitz_2021, title={Explicit multiobjective model predictive control for nonlinear systems  with symmetries}, volume={31(2)}, DOI={<a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>}, journal={International Journal of Robust and Nonlinear Control}, author={Ober-Blöbaum, Sina and Peitz, Sebastian}, year={2021}, pages={380–403} }","short":"S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear Control 31(2) (2021) 380–403.","apa":"Ober-Blöbaum, S., &#38; Peitz, S. (2021). Explicit multiobjective model predictive control for nonlinear systems  with symmetries. <i>International Journal of Robust and Nonlinear Control</i>, <i>31(2)</i>, 380–403. <a href=\"https://doi.org/10.1002/rnc.5281\">https://doi.org/10.1002/rnc.5281</a>"},"year":"2021"},{"citation":{"chicago":"Djema, Walid, Laetitia Giraldi, Sofya Maslovskaya, and Olivier Bernard. “Turnpike Features in Optimal Selection of Species Represented by Quota Models.” <i>Automatica</i> 132 (2021). <a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">https://doi.org/10.1016/j.automatica.2021.109804</a>.","ieee":"W. Djema, L. Giraldi, S. Maslovskaya, and O. Bernard, “Turnpike features in optimal selection of species represented by quota models,” <i>Automatica</i>, vol. 132, Art. no. 109804, 2021, doi: <a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>.","ama":"Djema W, Giraldi L, Maslovskaya S, Bernard O. Turnpike features in optimal selection of species represented by quota models. <i>Automatica</i>. 2021;132. doi:<a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>","bibtex":"@article{Djema_Giraldi_Maslovskaya_Bernard_2021, title={Turnpike features in optimal selection of species represented by quota models}, volume={132}, DOI={<a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>}, number={109804}, journal={Automatica}, publisher={Elsevier BV}, author={Djema, Walid and Giraldi, Laetitia and Maslovskaya, Sofya and Bernard, Olivier}, year={2021} }","mla":"Djema, Walid, et al. “Turnpike Features in Optimal Selection of Species Represented by Quota Models.” <i>Automatica</i>, vol. 132, 109804, Elsevier BV, 2021, doi:<a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>.","short":"W. Djema, L. Giraldi, S. Maslovskaya, O. Bernard, Automatica 132 (2021).","apa":"Djema, W., Giraldi, L., Maslovskaya, S., &#38; Bernard, O. (2021). Turnpike features in optimal selection of species represented by quota models. <i>Automatica</i>, <i>132</i>, Article 109804. <a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">https://doi.org/10.1016/j.automatica.2021.109804</a>"},"intvolume":"       132","year":"2021","publication_status":"published","publication_identifier":{"issn":["0005-1098"]},"doi":"10.1016/j.automatica.2021.109804","title":"Turnpike features in optimal selection of species represented by quota models","date_created":"2022-01-26T13:13:06Z","author":[{"full_name":"Djema, Walid","last_name":"Djema","first_name":"Walid"},{"first_name":"Laetitia","last_name":"Giraldi","full_name":"Giraldi, Laetitia"},{"first_name":"Sofya","last_name":"Maslovskaya","id":"87909","full_name":"Maslovskaya, Sofya"},{"first_name":"Olivier","last_name":"Bernard","full_name":"Bernard, Olivier"}],"volume":132,"publisher":"Elsevier BV","date_updated":"2022-01-26T13:15:33Z","status":"public","type":"journal_article","publication":"Automatica","language":[{"iso":"eng"}],"article_number":"109804","keyword":["Electrical and Electronic Engineering","Control and Systems Engineering"],"user_id":"87909","department":[{"_id":"636"}],"_id":"29543"},{"_id":"32810","user_id":"15540","department":[{"_id":"542"}],"article_number":"103451","keyword":["Discrete Mathematics and Combinatorics"],"language":[{"iso":"eng"}],"type":"journal_article","publication":"European Journal of Combinatorics","status":"public","date_updated":"2022-08-15T09:35:32Z","publisher":"Elsevier BV","author":[{"last_name":"Li","full_name":"Li, Jiaao","first_name":"Jiaao"},{"full_name":"Ma, Yulai","id":"92748","last_name":"Ma","first_name":"Yulai"},{"last_name":"Shi","full_name":"Shi, Yongtang","first_name":"Yongtang"},{"first_name":"Weifan","full_name":"Wang, Weifan","last_name":"Wang"},{"last_name":"Wu","full_name":"Wu, Yezhou","first_name":"Yezhou"}],"date_created":"2022-08-15T09:35:02Z","volume":100,"title":"On 3-flow-critical graphs","doi":"10.1016/j.ejc.2021.103451","publication_status":"published","publication_identifier":{"issn":["0195-6698"]},"year":"2021","citation":{"mla":"Li, Jiaao, et al. “On 3-Flow-Critical Graphs.” <i>European Journal of Combinatorics</i>, vol. 100, 103451, Elsevier BV, 2021, doi:<a href=\"https://doi.org/10.1016/j.ejc.2021.103451\">10.1016/j.ejc.2021.103451</a>.","bibtex":"@article{Li_Ma_Shi_Wang_Wu_2021, title={On 3-flow-critical graphs}, volume={100}, DOI={<a href=\"https://doi.org/10.1016/j.ejc.2021.103451\">10.1016/j.ejc.2021.103451</a>}, number={103451}, journal={European Journal of Combinatorics}, publisher={Elsevier BV}, author={Li, Jiaao and Ma, Yulai and Shi, Yongtang and Wang, Weifan and Wu, Yezhou}, year={2021} }","short":"J. Li, Y. Ma, Y. Shi, W. Wang, Y. Wu, European Journal of Combinatorics 100 (2021).","apa":"Li, J., Ma, Y., Shi, Y., Wang, W., &#38; Wu, Y. (2021). On 3-flow-critical graphs. <i>European Journal of Combinatorics</i>, <i>100</i>, Article 103451. <a href=\"https://doi.org/10.1016/j.ejc.2021.103451\">https://doi.org/10.1016/j.ejc.2021.103451</a>","chicago":"Li, Jiaao, Yulai Ma, Yongtang Shi, Weifan Wang, and Yezhou Wu. “On 3-Flow-Critical Graphs.” <i>European Journal of Combinatorics</i> 100 (2021). <a href=\"https://doi.org/10.1016/j.ejc.2021.103451\">https://doi.org/10.1016/j.ejc.2021.103451</a>.","ieee":"J. Li, Y. Ma, Y. Shi, W. Wang, and Y. Wu, “On 3-flow-critical graphs,” <i>European Journal of Combinatorics</i>, vol. 100, Art. no. 103451, 2021, doi: <a href=\"https://doi.org/10.1016/j.ejc.2021.103451\">10.1016/j.ejc.2021.103451</a>.","ama":"Li J, Ma Y, Shi Y, Wang W, Wu Y. On 3-flow-critical graphs. <i>European Journal of Combinatorics</i>. 2021;100. doi:<a href=\"https://doi.org/10.1016/j.ejc.2021.103451\">10.1016/j.ejc.2021.103451</a>"},"intvolume":"       100"},{"year":"2021","quality_controlled":"1","title":"Bifurcation preserving discretisations of optimal control problems","date_created":"2021-07-29T09:38:32Z","abstract":[{"text":"The first order optimality conditions of optimal control problems (OCPs) can\r\nbe regarded as boundary value problems for Hamiltonian systems. Variational or\r\nsymplectic discretisation methods are classically known for their excellent\r\nlong term behaviour. As boundary value problems are posed on intervals of\r\nfixed, moderate length, it is not immediately clear whether methods can profit\r\nfrom structure preservation in this context. When parameters are present,\r\nsolutions can undergo bifurcations, for instance, two solutions can merge and\r\nannihilate one another as parameters are varied. We will show that generic\r\nbifurcations of an OCP are preserved under discretisation when the OCP is\r\neither directly discretised to a discrete OCP (direct method) or translated\r\ninto a Hamiltonian boundary value problem using first order necessary\r\nconditions of optimality which is then solved using a symplectic integrator\r\n(indirect method). Moreover, certain bifurcations break when a non-symplectic\r\nscheme is used. The general phenomenon is illustrated on the example of a cut\r\nlocus of an ellipsoid.","lang":"eng"}],"file":[{"relation":"main_file","content_type":"application/pdf","access_level":"open_access","file_id":"22895","file_name":"ifacconf.pdf","file_size":3125220,"date_created":"2021-07-29T09:37:49Z","creator":"coffen","date_updated":"2021-07-29T09:37:49Z"}],"ddc":["510"],"keyword":["optimal control","catastrophe theory","bifurcations","variational methods","symplectic integrators"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["2107.13853"]},"citation":{"chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Bifurcation Preserving Discretisations of Optimal Control Problems.” IFAC-PapersOnLine, 2021. <a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>.","ieee":"C. Offen and S. Ober-Blöbaum, “Bifurcation preserving discretisations of optimal control problems,” vol. 54(19). pp. 334–339, 2021, doi: <a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>.","ama":"Offen C, Ober-Blöbaum S. Bifurcation preserving discretisations of optimal control problems. 2021;54(19):334-339. doi:<a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2021). <i>Bifurcation preserving discretisations of optimal control problems: Vol. 54(19)</i> (pp. 334–339). <a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>","mla":"Offen, Christian, and Sina Ober-Blöbaum. <i>Bifurcation Preserving Discretisations of Optimal Control Problems</i>. 2021, pp. 334–39, doi:<a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>.","short":"C. Offen, S. Ober-Blöbaum, 54(19) (2021) 334–339.","bibtex":"@article{Offen_Ober-Blöbaum_2021, series={IFAC-PapersOnLine}, title={Bifurcation preserving discretisations of optimal control problems}, volume={54(19)}, DOI={<a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2021}, pages={334–339}, collection={IFAC-PapersOnLine} }"},"page":"334-339","publication_status":"published","has_accepted_license":"1","publication_identifier":{"issn":["2405-8963"]},"related_material":{"link":[{"url":"https://doi.org/10.5281/zenodo.4562664","description":"GitHub/Zenodo","relation":"software"}]},"main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S2405896321021236","open_access":"1"}],"doi":"https://doi.org/10.1016/j.ifacol.2021.11.099","conference":{"start_date":"2021-10-11","name":"7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, LHMNC 2021","location":"Berlin, Germany","end_date":"2021-10-13"},"date_updated":"2023-11-29T10:19:41Z","oa":"1","author":[{"id":"85279","full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","first_name":"Christian"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494","last_name":"Ober-Blöbaum"}],"volume":"54(19)","status":"public","type":"conference","file_date_updated":"2021-07-29T09:37:49Z","_id":"22894","series_title":"IFAC-PapersOnLine","user_id":"15694","department":[{"_id":"636"}]},{"status":"public","type":"conference","_id":"21572","user_id":"15694","department":[{"_id":"636"}],"citation":{"bibtex":"@inproceedings{Ridderbusch_Offen_Ober-Blöbaum_Goulart_2021, title={Learning ODE Models with Qualitative Structure Using Gaussian Processes }, DOI={<a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">10.1109/CDC45484.2021.9683426</a>}, booktitle={2021 60th IEEE Conference on Decision and Control (CDC)}, publisher={IEEE}, author={Ridderbusch, Steffen and Offen, Christian and Ober-Blöbaum, Sina and Goulart, Paul}, year={2021}, pages={2896} }","mla":"Ridderbusch, Steffen, et al. “Learning ODE Models with Qualitative Structure Using Gaussian Processes .” <i>2021 60th IEEE Conference on Decision and Control (CDC)</i>, IEEE, 2021, p. 2896, doi:<a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">10.1109/CDC45484.2021.9683426</a>.","short":"S. Ridderbusch, C. Offen, S. Ober-Blöbaum, P. Goulart, in: 2021 60th IEEE Conference on Decision and Control (CDC), IEEE, 2021, p. 2896.","apa":"Ridderbusch, S., Offen, C., Ober-Blöbaum, S., &#38; Goulart, P. (2021). Learning ODE Models with Qualitative Structure Using Gaussian Processes . <i>2021 60th IEEE Conference on Decision and Control (CDC)</i>, 2896. <a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">https://doi.org/10.1109/CDC45484.2021.9683426</a>","ama":"Ridderbusch S, Offen C, Ober-Blöbaum S, Goulart P. Learning ODE Models with Qualitative Structure Using Gaussian Processes . In: <i>2021 60th IEEE Conference on Decision and Control (CDC)</i>. IEEE; 2021:2896. doi:<a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">10.1109/CDC45484.2021.9683426</a>","ieee":"S. Ridderbusch, C. Offen, S. Ober-Blöbaum, and P. Goulart, “Learning ODE Models with Qualitative Structure Using Gaussian Processes ,” in <i>2021 60th IEEE Conference on Decision and Control (CDC)</i>, Austin, TX, USA, 2021, p. 2896, doi: <a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">10.1109/CDC45484.2021.9683426</a>.","chicago":"Ridderbusch, Steffen, Christian Offen, Sina Ober-Blöbaum, and Paul Goulart. “Learning ODE Models with Qualitative Structure Using Gaussian Processes .” In <i>2021 60th IEEE Conference on Decision and Control (CDC)</i>, 2896. IEEE, 2021. <a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">https://doi.org/10.1109/CDC45484.2021.9683426</a>."},"page":"2896","publication_status":"published","publication_identifier":{"eisbn":["978-1-6654-3659-5"]},"related_material":{"link":[{"url":"https://github.com/Crown421/StructureGPs-paper","relation":"software","description":"GitHub"}]},"conference":{"start_date":"2021-12-14","name":"60th IEEE Conference on Decision and Control (CDC)","location":"Austin, TX, USA","end_date":"2021-12-17"},"doi":"10.1109/CDC45484.2021.9683426","date_updated":"2023-11-29T10:24:55Z","author":[{"first_name":"Steffen","full_name":"Ridderbusch, Steffen","last_name":"Ridderbusch"},{"first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","id":"85279","full_name":"Offen, Christian"},{"full_name":"Ober-Blöbaum, Sina","id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Paul","last_name":"Goulart","full_name":"Goulart, Paul"}],"publication":"2021 60th IEEE Conference on Decision and Control (CDC)","language":[{"iso":"eng"}],"external_id":{"arxiv":["2011.05364"]},"year":"2021","title":"Learning ODE Models with Qualitative Structure Using Gaussian Processes ","publisher":"IEEE","date_created":"2021-03-30T10:27:44Z"},{"status":"public","abstract":[{"text":"We propose a reachability approach for infinite and finite horizon multi-objective optimization problems for low-thrust spacecraft trajectory design. The main advantage of the proposed method is that the Pareto front can be efficiently constructed from the zero level set of the solution to a Hamilton-Jacobi-Bellman equation. We demonstrate the proposed method by applying it to a low-thrust spacecraft trajectory design problem. By deriving the analytic expression for the Hamiltonian and the optimal control policy, we are able to efficiently compute the backward reachable set and reconstruct the optimal trajectories. Furthermore, we show that any reconstructed trajectory will be guaranteed to be weakly Pareto optimal. The proposed method can be used as a benchmark for future research of applying reachability analysis to low-thrust spacecraft trajectory design.","lang":"eng"}],"type":"conference","language":[{"iso":"eng"}],"department":[{"_id":"636"}],"user_id":"15694","_id":"21592","external_id":{"arxiv":["2103.08813"]},"page":"1975-1980","citation":{"ieee":"N. Vertovec, S. Ober-Blöbaum, and K. Margellos, “Multi-objective minimum time optimal control for low-thrust trajectory design,” Rotterdam, the Netherlands, pp. 1975–1980.","chicago":"Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Multi-Objective Minimum Time Optimal Control for Low-Thrust Trajectory Design,” 1975–80, n.d.","ama":"Vertovec N, Ober-Blöbaum S, Margellos K. Multi-objective minimum time optimal control for low-thrust trajectory design. In: ; :1975-1980.","short":"N. Vertovec, S. Ober-Blöbaum, K. Margellos, in: n.d., pp. 1975–1980.","bibtex":"@inproceedings{Vertovec_Ober-Blöbaum_Margellos, title={Multi-objective minimum time optimal control for low-thrust trajectory design}, author={Vertovec, Nikolaus and Ober-Blöbaum, Sina and Margellos, Kostas}, pages={1975–1980} }","mla":"Vertovec, Nikolaus, et al. <i>Multi-Objective Minimum Time Optimal Control for Low-Thrust Trajectory Design</i>. pp. 1975–80.","apa":"Vertovec, N., Ober-Blöbaum, S., &#38; Margellos, K. (n.d.). <i>Multi-objective minimum time optimal control for low-thrust trajectory design</i>. 1975–1980."},"year":"2021","publication_status":"accepted","conference":{"start_date":"2021-06-29","name":"2021 European Control Conference (ECC)","location":"Rotterdam, the Netherlands","end_date":"2021-07-02"},"title":"Multi-objective minimum time optimal control for low-thrust trajectory design","date_created":"2021-04-03T03:00:35Z","author":[{"first_name":"Nikolaus","full_name":"Vertovec, Nikolaus","id":"87056","last_name":"Vertovec"},{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494","first_name":"Sina"},{"full_name":"Margellos, Kostas","last_name":"Margellos","first_name":"Kostas"}],"date_updated":"2023-11-29T10:26:49Z"},{"language":[{"iso":"eng"}],"_id":"29868","user_id":"15694","series_title":"J Nonlinear Sci ","department":[{"_id":"636"}],"status":"public","type":"conference","publication":"Nichtlineare Sci 31","title":"Fractional Damping Through Restricted Calculus of Variations","date_updated":"2023-11-29T10:23:46Z","author":[{"first_name":"F.","full_name":"Jiménez, F.","last_name":"Jiménez"},{"last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"}],"date_created":"2022-02-17T07:28:47Z","volume":46,"year":"2021","citation":{"apa":"Jiménez, F., &#38; Ober-Blöbaum, S. (2021). Fractional Damping Through Restricted Calculus of Variations. <i>Nichtlineare Sci 31</i>, <i>46</i>.","mla":"Jiménez, F., and Sina Ober-Blöbaum. “Fractional Damping Through Restricted Calculus of Variations.” <i>Nichtlineare Sci 31</i>, vol. 46, 2021.","short":"F. Jiménez, S. Ober-Blöbaum, in: Nichtlineare Sci 31, 2021.","bibtex":"@inproceedings{Jiménez_Ober-Blöbaum_2021, series={J Nonlinear Sci }, title={Fractional Damping Through Restricted Calculus of Variations}, volume={46}, booktitle={Nichtlineare Sci 31}, author={Jiménez, F. and Ober-Blöbaum, Sina}, year={2021}, collection={J Nonlinear Sci } }","ieee":"F. Jiménez and S. Ober-Blöbaum, “Fractional Damping Through Restricted Calculus of Variations,” in <i>Nichtlineare Sci 31</i>, 2021, vol. 46.","chicago":"Jiménez, F., and Sina Ober-Blöbaum. “Fractional Damping Through Restricted Calculus of Variations.” In <i>Nichtlineare Sci 31</i>, Vol. 46. J Nonlinear Sci , 2021.","ama":"Jiménez F, Ober-Blöbaum S. Fractional Damping Through Restricted Calculus of Variations. In: <i>Nichtlineare Sci 31</i>. Vol 46. J Nonlinear Sci . ; 2021."},"intvolume":"        46"}]