[{"oa":"1","date_updated":"2023-12-21T09:47:22Z","_id":"32097","citation":{"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.","mla":"Weich, Tobias, et al. “SRB Measures of Anosov Actions.” 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} }","short":"T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, Journal of Differential Geometry (to Appear) -- ArXiv:2103.12127 (2024).","ieee":"T. Weich, Y. Guedes Bonthonneau, and C. Guillarmou, “SRB Measures of Anosov Actions,” Journal of Differential Geometry (to appear) -- arXiv:2103.12127, 2024."},"year":"2024","type":"journal_article","language":[{"iso":"eng"}],"ddc":["510"],"title":"SRB Measures of Anosov Actions","user_id":"49178","external_id":{"arxiv":["https://arxiv.org/abs/2103.12127"]},"has_accepted_license":"1","status":"public","date_created":"2022-06-22T09:56:23Z","author":[{"id":"49178","last_name":"Weich","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","first_name":"Tobias"},{"first_name":"Yannick","full_name":"Guedes Bonthonneau, Yannick","last_name":"Guedes Bonthonneau"},{"first_name":"Colin","full_name":"Guillarmou, Colin","last_name":"Guillarmou"}],"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","file":[{"file_name":"2103.12127.pdf","date_created":"2022-06-22T09:56:08Z","access_level":"open_access","creator":"weich","file_id":"32098","file_size":745870,"relation":"main_file","content_type":"application/pdf","date_updated":"2022-06-22T09:56:08Z"}]},{"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"}],"article_type":"original","ddc":["510"],"user_id":"85279","file_date_updated":"2024-01-09T11:19:49Z","publication":"Chaos","author":[{"first_name":"Christian","orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","last_name":"Offen","id":"85279"},{"id":"16494","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"}],"publisher":"AIP Publishing","quality_controlled":"1","file":[{"file_size":13222105,"title":"Accepted Manuscript Chaos","file_id":"50376","creator":"coffen","content_type":"application/pdf","date_updated":"2024-01-09T10:48:38Z","relation":"main_file","date_created":"2024-01-09T10:48:38Z","file_name":"Accepted manuscript with AIP banner CHA23-AR-01370.pdf","access_level":"open_access"},{"access_level":"open_access","date_created":"2024-01-09T11:19:49Z","file_name":"LDensityPDE_AIP.pdf","content_type":"application/pdf","date_updated":"2024-01-09T11:19:49Z","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.","file_size":12960884,"creator":"coffen","file_id":"50390","title":"Learning of discrete models of variational PDEs from data"}],"volume":34,"date_created":"2023-08-10T08:24:48Z","status":"public","has_accepted_license":"1","intvolume":" 34","_id":"46469","article_number":"013104","issue":"1","year":"2024","type":"journal_article","citation":{"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","ama":"Offen C, Ober-Blöbaum S. Learning of discrete models of variational PDEs from data. Chaos. 2024;34(1). doi: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.","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} }","short":"C. Offen, S. Ober-Blöbaum, Chaos 34 (2024).","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."},"external_id":{"arxiv":["2308.05082 "]},"title":"Learning of discrete models of variational PDEs from data","related_material":{"link":[{"description":"GitHub","relation":"software","url":"https://github.com/Christian-Offen/DLNN_pde"}]},"department":[{"_id":"636"}],"publication_identifier":{"issn":["1054-1500"]},"publication_status":"published","date_updated":"2024-01-09T11:29:06Z","doi":"10.1063/5.0172287","oa":"1","language":[{"iso":"eng"}]},{"department":[{"_id":"34"},{"_id":"10"},{"_id":"643"}],"editor":[{"last_name":"Efing","full_name":"Efing, Christian","first_name":"Christian"},{"first_name":"Zeynep","full_name":"Kalkavan-Aydin, Zeynep","last_name":"Kalkavan-Aydin"}],"publication_identifier":{"isbn":["978-3-11-074544-3"]},"publication_status":"published","place":"Berlin","title":"31 Sprachbildung im berufsbezogenen Mathematikunterricht.","series_title":"DaZ-Handbücher","language":[{"iso":"ger"}],"date_updated":"2024-01-17T11:07:21Z","oa":"1","author":[{"last_name":"Prediger","full_name":"Prediger, Susanne","first_name":"Susanne"},{"last_name":"Wessel","id":"85190","first_name":"Lena","full_name":"Wessel, Lena"}],"publisher":"DE GRUYTER","publication":"Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis","status":"public","date_created":"2024-01-17T10:58:04Z","volume":"Band 3","user_id":"37888","main_file_link":[{"url":"https://www.degruyter.com/document/doi/10.1515/9783110745504/pdf?licenseType=restricted#page=381","open_access":"1"}],"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."},"page":"363-372","_id":"50554"},{"_id":"51208","date_updated":"2024-02-08T08:05:54Z","doi":"10.1007/s10589-024-00552-0","language":[{"iso":"eng"}],"type":"journal_article","year":"2024","citation":{"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} }","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.","ama":"Gebken B. A note on the convergence of deterministic gradient sampling in nonsmooth optimization. Computational Optimization and Applications. Published online 2024. doi:10.1007/s10589-024-00552-0","apa":"Gebken, B. (2024). A note on the convergence of deterministic gradient sampling in nonsmooth optimization. Computational Optimization and Applications. https://doi.org/10.1007/s10589-024-00552-0","ieee":"B. Gebken, “A note on the convergence of deterministic gradient sampling in nonsmooth optimization,” Computational Optimization and Applications, 2024, doi: 10.1007/s10589-024-00552-0.","short":"B. Gebken, Computational Optimization and Applications (2024)."},"abstract":[{"lang":"eng","text":"AbstractApproximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions."}],"user_id":"32643","title":"A note on the convergence of deterministic gradient sampling in nonsmooth optimization","keyword":["Applied Mathematics","Computational Mathematics","Control and Optimization"],"publication":"Computational Optimization and Applications","department":[{"_id":"101"}],"publisher":"Springer Science and Business Media LLC","author":[{"id":"32643","last_name":"Gebken","full_name":"Gebken, Bennet","first_name":"Bennet"}],"date_created":"2024-02-07T07:23:23Z","status":"public","publication_identifier":{"issn":["0926-6003","1573-2894"]},"publication_status":"published"},{"_id":"51204","date_updated":"2024-02-11T19:56:35Z","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.","ama":"Lutsko C, Weich T, Wolf LL. Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces. arXiv:240202530. Published online 2024.","short":"C. Lutsko, T. Weich, L.L. Wolf, ArXiv:2402.02530 (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."},"year":"2024","type":"preprint","language":[{"iso":"eng"}],"title":"Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces","user_id":"49178","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."}],"status":"public","date_created":"2024-02-06T20:35:36Z","author":[{"full_name":"Lutsko, Christopher","first_name":"Christopher","last_name":"Lutsko"},{"last_name":"Weich","first_name":"Tobias","full_name":"Weich, Tobias"},{"first_name":"Lasse Lennart","full_name":"Wolf, Lasse Lennart","last_name":"Wolf","id":"45027"}],"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"publication":"arXiv:2402.02530"},{"article_number":"110319","issue":"7","intvolume":" 286","_id":"51374","type":"journal_article","year":"2024","citation":{"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.","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.","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} }","short":"D. Hasler, B. Hinrichs, O. Siebert, Journal of Functional Analysis 286 (2024).","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."},"user_id":"99427","extern":"1","volume":286,"status":"public","date_created":"2024-02-18T12:31:28Z","author":[{"first_name":"David","full_name":"Hasler, David","last_name":"Hasler"},{"first_name":"Benjamin","orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin","last_name":"Hinrichs","id":"99427"},{"last_name":"Siebert","first_name":"Oliver","full_name":"Siebert, Oliver"}],"publisher":"Elsevier BV","publication":"Journal of Functional Analysis","keyword":["Analysis"],"doi":"10.1016/j.jfa.2024.110319","date_updated":"2024-02-18T12:32:23Z","language":[{"iso":"eng"}],"title":"Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively","external_id":{"arxiv":["2302.06998"]},"publication_status":"published","publication_identifier":{"issn":["0022-1236"]},"department":[{"_id":"799"}]},{"date_updated":"2024-02-19T06:25:13Z","_id":"32101","oa":"1","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.","apa":"Weich, T., Guedes Bonthonneau, Y., Guillarmou, C., & Hilgert, J. (2024). Ruelle-Taylor resonaces of Anosov actions. J. Europ. Math. Soc., 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.","mla":"Weich, Tobias, et al. “Ruelle-Taylor Resonaces of Anosov Actions.” J. Europ. Math. Soc., 2024, pp. 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} }"},"type":"journal_article","year":"2024","page":"1-36","language":[{"iso":"eng"}],"ddc":["510"],"title":"Ruelle-Taylor resonaces of Anosov actions","user_id":"49063","author":[{"first_name":"Tobias","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias","last_name":"Weich","id":"49178"},{"full_name":"Guedes Bonthonneau, Yannick","first_name":"Yannick","last_name":"Guedes Bonthonneau"},{"full_name":"Guillarmou, Colin","first_name":"Colin","last_name":"Guillarmou"},{"id":"220","last_name":"Hilgert","full_name":"Hilgert, Joachim","first_name":"Joachim"}],"file_date_updated":"2022-06-22T09:56:47Z","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}],"publication":"J. Europ. Math. Soc.","file":[{"access_level":"open_access","file_name":"2007.14275.pdf","date_created":"2022-06-22T09:56:47Z","date_updated":"2022-06-22T09:56:47Z","content_type":"application/pdf","relation":"main_file","file_size":796410,"creator":"weich","file_id":"32102"}],"publication_status":"published","status":"public","has_accepted_license":"1","date_created":"2022-06-22T09:56:51Z"},{"department":[{"_id":"91"}],"author":[{"first_name":"Joachim","full_name":"Hilgert, Joachim","last_name":"Hilgert","id":"220"}],"date_created":"2024-02-19T10:31:51Z","status":"public","publication_status":"published","user_id":"49063","title":"Quantum-Classical Correspondences for Locally Symmetric Spaces","main_file_link":[{"url":"https://arxiv.org/pdf/2303.00578.pdf","open_access":"1"}],"language":[{"iso":"eng"}],"year":"2024","type":"preprint","citation":{"bibtex":"@article{Hilgert_2024, title={Quantum-Classical Correspondences for Locally Symmetric Spaces}, author={Hilgert, Joachim}, year={2024} }","mla":"Hilgert, Joachim. Quantum-Classical Correspondences for Locally Symmetric Spaces. 2024.","apa":"Hilgert, J. (2024). Quantum-Classical Correspondences for Locally Symmetric Spaces.","ama":"Hilgert J. Quantum-Classical Correspondences for Locally Symmetric Spaces. Published online 2024.","chicago":"Hilgert, Joachim. “Quantum-Classical Correspondences for Locally Symmetric Spaces,” 2024.","ieee":"J. Hilgert, “Quantum-Classical Correspondences for Locally Symmetric Spaces.” 2024.","short":"J. Hilgert, (2024)."},"date_updated":"2024-02-19T10:32:07Z","_id":"51501","oa":"1"},{"abstract":[{"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.","lang":"eng"}],"user_id":"56399","title":"Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems","publication":"Journal of Optimization Theory and Applications","department":[{"_id":"101"},{"_id":"655"}],"publisher":"Springer","author":[{"id":"56399","last_name":"Sonntag","full_name":"Sonntag, Konstantin","orcid":"https://orcid.org/0000-0003-3384-3496","first_name":"Konstantin"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427"}],"date_created":"2023-07-12T06:35:58Z","status":"public","publication_status":"published","date_updated":"2024-02-21T10:13:33Z","_id":"46019","oa":"1","doi":"10.1007/s10957-024-02389-3","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10957-024-02389-3.pdf","open_access":"1"}],"language":[{"iso":"eng"}],"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.","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.","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","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"},"year":"2024","type":"journal_article"},{"_id":"51334","date_updated":"2024-02-21T10:21:03Z","oa":"1","main_file_link":[{"url":"https://arxiv.org/abs/2402.06376","open_access":"1"}],"citation":{"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} }","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."},"type":"preprint","year":"2024","language":[{"iso":"eng"}],"external_id":{"arxiv":["\t2402.06376"]},"abstract":[{"lang":"eng","text":"The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points, where in each iteration, an approximation of the subdifferential is computed in an efficient manner and then used to compute a common descent direction for all objective functions. To prove convergence, we present some new optimality results for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these, we can show that every accumulation point of the sequence generated by our algorithm is Pareto critical under common assumptions. Computational efficiency for finding Pareto critical points is numerically demonstrated for multiobjective optimal control of an obstacle problem."}],"title":"A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces","user_id":"56399","author":[{"last_name":"Sonntag","id":"56399","first_name":"Konstantin","orcid":"https://orcid.org/0000-0003-3384-3496","full_name":"Sonntag, Konstantin"},{"id":"32643","last_name":"Gebken","full_name":"Gebken, Bennet","first_name":"Bennet"},{"first_name":"Georg","full_name":"Müller, Georg","last_name":"Müller"},{"orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian","id":"47427","last_name":"Peitz"},{"first_name":"Stefan","full_name":"Volkwein, Stefan","last_name":"Volkwein"}],"department":[{"_id":"101"},{"_id":"655"}],"publication":"arXiv:2402.06376","status":"public","has_accepted_license":"1","date_created":"2024-02-13T09:35:26Z"}]