--- _id: '32097' author: - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 - first_name: Yannick full_name: Guedes Bonthonneau, Yannick last_name: Guedes Bonthonneau - first_name: Colin full_name: Guillarmou, Colin last_name: Guillarmou citation: 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. 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} }' chicago: Weich, Tobias, Yannick Guedes Bonthonneau, and Colin Guillarmou. “SRB Measures of Anosov Actions.” 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. mla: Weich, Tobias, et al. “SRB Measures of Anosov Actions.” Journal of Differential Geometry (to Appear) --  ArXiv:2103.12127, 2024. short: T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, Journal of Differential Geometry (to Appear) --  ArXiv:2103.12127 (2024). date_created: 2022-06-22T09:56:23Z date_updated: 2023-12-21T09:47:22Z ddc: - '510' department: - _id: '10' - _id: '623' - _id: '548' external_id: arxiv: - https://arxiv.org/abs/2103.12127 file: - access_level: open_access content_type: application/pdf creator: weich date_created: 2022-06-22T09:56:08Z date_updated: 2022-06-22T09:56:08Z file_id: '32098' file_name: 2103.12127.pdf file_size: 745870 relation: main_file file_date_updated: 2022-06-22T09:56:08Z has_accepted_license: '1' language: - iso: eng oa: '1' publication: Journal of Differential Geometry (to appear) -- arXiv:2103.12127 status: public title: SRB Measures of Anosov Actions type: journal_article user_id: '49178' year: '2024' ... --- _id: '46469' abstract: - lang: eng 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. ' article_number: '013104' article_type: original author: - first_name: Christian full_name: Offen, Christian id: '85279' last_name: Offen orcid: 0000-0002-5940-8057 - first_name: Sina full_name: Ober-Blöbaum, Sina id: '16494' last_name: Ober-Blöbaum citation: ama: Offen C, Ober-Blöbaum S. Learning of discrete models of variational PDEs from data. Chaos. 2024;34(1). doi:10.1063/5.0172287 apa: Offen, C., & Ober-Blöbaum, S. (2024). Learning of discrete models of variational PDEs from data. Chaos, 34(1), Article 013104. https://doi.org/10.1063/5.0172287 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} }' chicago: Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational PDEs from Data.” Chaos 34, no. 1 (2024). https://doi.org/10.1063/5.0172287. ieee: 'C. Offen and S. Ober-Blöbaum, “Learning of discrete models of variational PDEs from data,” Chaos, vol. 34, no. 1, Art. no. 013104, 2024, doi: 10.1063/5.0172287.' 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. short: C. Offen, S. Ober-Blöbaum, Chaos 34 (2024). date_created: 2023-08-10T08:24:48Z date_updated: 2024-01-09T11:29:06Z ddc: - '510' department: - _id: '636' doi: 10.1063/5.0172287 external_id: arxiv: - '2308.05082 ' file: - access_level: open_access content_type: application/pdf creator: coffen date_created: 2024-01-09T10:48:38Z date_updated: 2024-01-09T10:48:38Z file_id: '50376' file_name: Accepted manuscript with AIP banner CHA23-AR-01370.pdf file_size: 13222105 relation: main_file title: Accepted Manuscript Chaos - access_level: open_access content_type: application/pdf creator: coffen date_created: 2024-01-09T11:19:49Z date_updated: 2024-01-09T11:19:49Z description: |- 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. file_id: '50390' file_name: LDensityPDE_AIP.pdf file_size: 12960884 relation: main_file title: Learning of discrete models of variational PDEs from data file_date_updated: 2024-01-09T11:19:49Z has_accepted_license: '1' intvolume: ' 34' issue: '1' language: - iso: eng oa: '1' publication: Chaos publication_identifier: issn: - 1054-1500 publication_status: published publisher: AIP Publishing quality_controlled: '1' related_material: link: - description: GitHub relation: software url: https://github.com/Christian-Offen/DLNN_pde status: public title: Learning of discrete models of variational PDEs from data type: journal_article user_id: '85279' volume: 34 year: '2024' ... --- _id: '50554' author: - first_name: Susanne full_name: Prediger, Susanne last_name: Prediger - first_name: Lena full_name: Wessel, Lena id: '85190' last_name: Wessel citation: 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.' 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.' 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} }' 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.' 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.' 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. 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.' date_created: 2024-01-17T10:58:04Z date_updated: 2024-01-17T11:07:21Z department: - _id: '34' - _id: '10' - _id: '643' editor: - first_name: Christian full_name: Efing, Christian last_name: Efing - first_name: Zeynep full_name: Kalkavan-Aydin, Zeynep last_name: Kalkavan-Aydin language: - iso: ger main_file_link: - open_access: '1' url: https://www.degruyter.com/document/doi/10.1515/9783110745504/pdf?licenseType=restricted#page=381 oa: '1' page: 363-372 place: Berlin publication: Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis publication_identifier: isbn: - 978-3-11-074544-3 publication_status: published publisher: DE GRUYTER series_title: DaZ-Handbücher status: public title: 31 Sprachbildung im berufsbezogenen Mathematikunterricht. type: book_chapter user_id: '37888' volume: Band 3 year: '2024' ... --- _id: '51208' 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. author: - first_name: Bennet full_name: Gebken, Bennet id: '32643' last_name: Gebken citation: 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 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. 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.' 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. short: B. Gebken, Computational Optimization and Applications (2024). date_created: 2024-02-07T07:23:23Z date_updated: 2024-02-08T08:05:54Z department: - _id: '101' doi: 10.1007/s10589-024-00552-0 keyword: - Applied Mathematics - Computational Mathematics - Control and Optimization language: - iso: eng publication: Computational Optimization and Applications publication_identifier: issn: - 0926-6003 - 1573-2894 publication_status: published publisher: Springer Science and Business Media LLC status: public title: A note on the convergence of deterministic gradient sampling in nonsmooth optimization type: journal_article user_id: '32643' year: '2024' ... --- _id: '51204' 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." author: - first_name: Christopher full_name: Lutsko, Christopher last_name: Lutsko - first_name: Tobias full_name: Weich, Tobias last_name: Weich - first_name: Lasse Lennart full_name: Wolf, Lasse Lennart id: '45027' last_name: Wolf citation: ama: Lutsko C, Weich T, Wolf LL. Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces. arXiv:240202530. Published online 2024. apa: Lutsko, C., Weich, T., & Wolf, L. L. (2024). Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces. In arXiv:2402.02530. 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} }' 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. 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. mla: Lutsko, Christopher, et al. “Polyhedral Bounds on the Joint Spectrum and Temperedness of Locally  Symmetric Spaces.” ArXiv:2402.02530, 2024. short: C. Lutsko, T. Weich, L.L. Wolf, ArXiv:2402.02530 (2024). date_created: 2024-02-06T20:35:36Z date_updated: 2024-02-11T19:56:35Z department: - _id: '10' - _id: '623' - _id: '548' external_id: arxiv: - '2402.02530' language: - iso: eng publication: arXiv:2402.02530 status: public title: Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces type: preprint user_id: '49178' year: '2024' ... --- _id: '51374' article_number: '110319' author: - first_name: David full_name: Hasler, David last_name: Hasler - first_name: Benjamin full_name: Hinrichs, Benjamin id: '99427' last_name: Hinrichs orcid: 0000-0001-9074-1205 - first_name: Oliver full_name: Siebert, Oliver last_name: Siebert citation: 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 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 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} }' chicago: Hasler, David, Benjamin Hinrichs, and Oliver Siebert. “Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively.” Journal of Functional Analysis 286, no. 7 (2024). https://doi.org/10.1016/j.jfa.2024.110319. ieee: 'D. Hasler, B. Hinrichs, and O. Siebert, “Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively,” Journal of Functional Analysis, vol. 286, no. 7, Art. no. 110319, 2024, doi: 10.1016/j.jfa.2024.110319.' 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. short: D. Hasler, B. Hinrichs, O. Siebert, Journal of Functional Analysis 286 (2024). date_created: 2024-02-18T12:31:28Z date_updated: 2024-02-18T12:32:23Z department: - _id: '799' doi: 10.1016/j.jfa.2024.110319 extern: '1' external_id: arxiv: - '2302.06998' intvolume: ' 286' issue: '7' keyword: - Analysis language: - iso: eng publication: Journal of Functional Analysis publication_identifier: issn: - 0022-1236 publication_status: published publisher: Elsevier BV status: public title: Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively type: journal_article user_id: '99427' volume: 286 year: '2024' ... --- _id: '32101' author: - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 - first_name: Yannick full_name: Guedes Bonthonneau, Yannick last_name: Guedes Bonthonneau - first_name: Colin full_name: Guillarmou, Colin last_name: Guillarmou - first_name: Joachim full_name: Hilgert, Joachim id: '220' last_name: Hilgert citation: ama: Weich T, Guedes Bonthonneau Y, Guillarmou C, Hilgert J. Ruelle-Taylor resonaces of Anosov actions. J Europ Math Soc. Published online 2024:1-36. apa: Weich, T., Guedes Bonthonneau, Y., Guillarmou, C., & Hilgert, J. (2024). Ruelle-Taylor resonaces of Anosov actions. J. Europ. Math. Soc., 1–36. bibtex: '@article{Weich_Guedes Bonthonneau_Guillarmou_Hilgert_2024, title={Ruelle-Taylor resonaces of Anosov actions}, journal={J. Europ. Math. Soc.}, author={Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin and Hilgert, Joachim}, year={2024}, pages={1–36} }' chicago: Weich, Tobias, Yannick Guedes Bonthonneau, Colin Guillarmou, and Joachim Hilgert. “Ruelle-Taylor Resonaces of Anosov Actions.” 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. mla: Weich, Tobias, et al. “Ruelle-Taylor Resonaces of Anosov Actions.” J. Europ. Math. Soc., 2024, pp. 1–36. short: T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, J. Hilgert, J. Europ. Math. Soc. (2024) 1–36. date_created: 2022-06-22T09:56:51Z date_updated: 2024-02-19T06:25:13Z ddc: - '510' department: - _id: '10' - _id: '623' - _id: '548' - _id: '91' file: - access_level: open_access content_type: application/pdf creator: weich date_created: 2022-06-22T09:56:47Z date_updated: 2022-06-22T09:56:47Z file_id: '32102' file_name: 2007.14275.pdf file_size: 796410 relation: main_file file_date_updated: 2022-06-22T09:56:47Z has_accepted_license: '1' language: - iso: eng oa: '1' page: 1-36 publication: J. Europ. Math. Soc. publication_status: published status: public title: Ruelle-Taylor resonaces of Anosov actions type: journal_article user_id: '49063' year: '2024' ... --- _id: '51501' author: - first_name: Joachim full_name: Hilgert, Joachim id: '220' last_name: Hilgert citation: ama: Hilgert J. Quantum-Classical Correspondences for Locally Symmetric Spaces. Published online 2024. apa: Hilgert, J. (2024). Quantum-Classical Correspondences for Locally Symmetric Spaces. bibtex: '@article{Hilgert_2024, title={Quantum-Classical Correspondences for Locally Symmetric Spaces}, author={Hilgert, Joachim}, year={2024} }' chicago: Hilgert, Joachim. “Quantum-Classical Correspondences for Locally Symmetric Spaces,” 2024. ieee: J. Hilgert, “Quantum-Classical Correspondences for Locally Symmetric Spaces.” 2024. mla: Hilgert, Joachim. Quantum-Classical Correspondences for Locally Symmetric Spaces. 2024. short: J. Hilgert, (2024). date_created: 2024-02-19T10:31:51Z date_updated: 2024-02-19T10:32:07Z department: - _id: '91' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/pdf/2303.00578.pdf oa: '1' publication_status: published status: public title: Quantum-Classical Correspondences for Locally Symmetric Spaces type: preprint user_id: '49063' year: '2024' ... --- _id: '46019' abstract: - lang: eng text: We derive efficient algorithms to compute weakly Pareto optimal solutions for smooth, convex and unconstrained multiobjective optimization problems in general Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical system in the multiobjective setting, which trajectories converge weakly to Pareto optimal solutions. Discretization of this system yields an inertial multiobjective algorithm which generates sequences that converge weakly to Pareto optimal solutions. We employ Nesterov acceleration to define an algorithm with an improved convergence rate compared to the plain multiobjective steepest descent method (Algorithm 1). A further improvement in terms of efficiency is achieved by avoiding the solution of a quadratic subproblem to compute a common step direction for all objective functions, which is usually required in first-order methods. Using a different discretization of our inertial gradient-like dynamical system, we obtain an accelerated multiobjective gradient method that does not require the solution of a subproblem in each step (Algorithm 2). While this algorithm does not converge in general, it yields good results on test problems while being faster than standard steepest descent. author: - first_name: Konstantin full_name: Sonntag, Konstantin id: '56399' last_name: Sonntag orcid: https://orcid.org/0000-0003-3384-3496 - first_name: Sebastian full_name: Peitz, Sebastian id: '47427' last_name: Peitz orcid: 0000-0002-3389-793X citation: ama: Sonntag K, Peitz S. Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems. Journal of Optimization Theory and Applications. Published online 2024. doi:10.1007/s10957-024-02389-3 apa: Sonntag, K., & Peitz, S. (2024). Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems. Journal of Optimization Theory and Applications. https://doi.org/10.1007/s10957-024-02389-3 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} }' 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. 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.' 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. short: K. Sonntag, S. Peitz, Journal of Optimization Theory and Applications (2024). date_created: 2023-07-12T06:35:58Z date_updated: 2024-02-21T10:13:33Z department: - _id: '101' - _id: '655' doi: 10.1007/s10957-024-02389-3 language: - iso: eng main_file_link: - open_access: '1' url: https://link.springer.com/content/pdf/10.1007/s10957-024-02389-3.pdf oa: '1' publication: Journal of Optimization Theory and Applications publication_status: published publisher: Springer status: public title: Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems type: journal_article user_id: '56399' year: '2024' ... --- _id: '51334' 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. author: - first_name: Konstantin full_name: Sonntag, Konstantin id: '56399' last_name: Sonntag orcid: https://orcid.org/0000-0003-3384-3496 - first_name: Bennet full_name: Gebken, Bennet id: '32643' last_name: Gebken - first_name: Georg full_name: Müller, Georg last_name: Müller - first_name: Sebastian full_name: Peitz, Sebastian id: '47427' last_name: Peitz orcid: 0000-0002-3389-793X - first_name: Stefan full_name: Volkwein, Stefan last_name: Volkwein 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. bibtex: '@article{Sonntag_Gebken_Müller_Peitz_Volkwein_2024, title={A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces}, journal={arXiv:2402.06376}, author={Sonntag, Konstantin and Gebken, Bennet and Müller, Georg and Peitz, Sebastian and Volkwein, Stefan}, year={2024} }' chicago: Sonntag, Konstantin, Bennet Gebken, Georg Müller, Sebastian Peitz, and Stefan Volkwein. “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.” ArXiv:2402.06376, 2024. 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. mla: Sonntag, Konstantin, et al. “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.” ArXiv:2402.06376, 2024. short: K. Sonntag, B. Gebken, G. Müller, S. Peitz, S. Volkwein, ArXiv:2402.06376 (2024). date_created: 2024-02-13T09:35:26Z date_updated: 2024-02-21T10:21:03Z department: - _id: '101' - _id: '655' external_id: arxiv: - "\t2402.06376" has_accepted_license: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2402.06376 oa: '1' publication: arXiv:2402.06376 status: public title: A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces type: preprint user_id: '56399' year: '2024' ...