[{"external_id":{"arxiv":["2507.06024"]},"date_created":"2026-01-06T18:28:18Z","type":"preprint","department":[{"_id":"636"}],"publication":"arXiv:2507.06024","citation":{"chicago":"Konopik, Michael, Sigrid Leyendecker, Sofya Maslovskaya, Sina Ober-Blöbaum Sina Ober-Blöbaum, and Rodrigo T. Sato Martín de Almagro. “Second Order Optimality Conditions in a New Lagrangian Formulation for Optimal Control Problems.” <i>ArXiv:2507.06024</i>, 2025.","short":"M. Konopik, S. Leyendecker, S. Maslovskaya, S.O.-B. Sina Ober-Blöbaum, R.T.S.M. de Almagro, ArXiv:2507.06024 (2025).","apa":"Konopik, M., Leyendecker, S., Maslovskaya, S., Sina Ober-Blöbaum, S. O.-B., &#38; Almagro, R. T. S. M. de. (2025). Second order optimality conditions in a new Lagrangian formulation for optimal control problems. In <i>arXiv:2507.06024</i>.","ieee":"M. Konopik, S. Leyendecker, S. Maslovskaya, S. O.-B. Sina Ober-Blöbaum, and R. T. S. M. de Almagro, “Second order optimality conditions in a new Lagrangian formulation for optimal control problems,” <i>arXiv:2507.06024</i>. 2025.","ama":"Konopik M, Leyendecker S, Maslovskaya S, Sina Ober-Blöbaum SO-B, Almagro RTSM de. Second order optimality conditions in a new Lagrangian formulation for optimal control problems. <i>arXiv:250706024</i>. Published online 2025.","bibtex":"@article{Konopik_Leyendecker_Maslovskaya_Sina Ober-Blöbaum_Almagro_2025, title={Second order optimality conditions in a new Lagrangian formulation for optimal control problems}, journal={arXiv:2507.06024}, author={Konopik, Michael and Leyendecker, Sigrid and Maslovskaya, Sofya and Sina Ober-Blöbaum, Sina Ober-Blöbaum and Almagro, Rodrigo T. Sato Martín de}, year={2025} }","mla":"Konopik, Michael, et al. “Second Order Optimality Conditions in a New Lagrangian Formulation for Optimal Control Problems.” <i>ArXiv:2507.06024</i>, 2025."},"abstract":[{"lang":"eng","text":"It has been shown recently that optimal control problems with the dynamical constraint given by a second order system admit a regular Lagrangian formulation. This implies that the optimality conditions can be obtained in a new form based on the variational approach. In this paper we extend the first order necessary optimality conditions obtained previously to second order optimality conditions. This results in a complete characterization of the optimality conditions in a new Lagrangian form."}],"_id":"63510","language":[{"iso":"eng"}],"user_id":"87909","status":"public","year":"2025","title":"Second order optimality conditions in a new Lagrangian formulation for optimal control problems","author":[{"full_name":"Konopik, Michael","first_name":"Michael","last_name":"Konopik"},{"last_name":"Leyendecker","first_name":"Sigrid","full_name":"Leyendecker, Sigrid"},{"last_name":"Maslovskaya","first_name":"Sofya","full_name":"Maslovskaya, Sofya"},{"full_name":"Sina Ober-Blöbaum, Sina Ober-Blöbaum","first_name":"Sina Ober-Blöbaum","last_name":"Sina Ober-Blöbaum"},{"full_name":"Almagro, Rodrigo T. Sato Martín de","last_name":"Almagro","first_name":"Rodrigo T. Sato Martín de"}],"date_updated":"2026-01-06T18:29:15Z"},{"intvolume":"        36","date_updated":"2026-01-06T18:26:57Z","author":[{"first_name":"Michael","last_name":"Konopik","full_name":"Konopik, Michael"},{"full_name":"T. Sato Martín de Almagro, Rodrigo","first_name":"Rodrigo","last_name":"T. Sato Martín de Almagro"},{"id":"87909","full_name":"Maslovskaya, Sofya","first_name":"Sofya","last_name":"Maslovskaya"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494"},{"first_name":"Sigrid","last_name":"Leyendecker","full_name":"Leyendecker, Sigrid"}],"status":"public","title":"Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term","year":"2025","volume":36,"doi":"10.1007/s00332-025-10229-5","user_id":"87909","_id":"59797","language":[{"iso":"eng"}],"citation":{"apa":"Konopik, M., T. Sato Martín de Almagro, R., Maslovskaya, S., Ober-Blöbaum, S., &#38; Leyendecker, S. (2025). Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term. <i>Journal of Nonlinear Science</i>, <i>36</i>(11). <a href=\"https://doi.org/10.1007/s00332-025-10229-5\">https://doi.org/10.1007/s00332-025-10229-5</a>","mla":"Konopik, Michael, et al. “Variational Integrators for a New Lagrangian Approach to Control Affine Systems with a Quadratic Lagrange Term.” <i>Journal of Nonlinear Science</i>, vol. 36, no. 11, 2025, doi:<a href=\"https://doi.org/10.1007/s00332-025-10229-5\">10.1007/s00332-025-10229-5</a>.","ieee":"M. Konopik, R. T. Sato Martín de Almagro, S. Maslovskaya, S. Ober-Blöbaum, and S. Leyendecker, “Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term,” <i>Journal of Nonlinear Science</i>, vol. 36, no. 11, 2025, doi: <a href=\"https://doi.org/10.1007/s00332-025-10229-5\">10.1007/s00332-025-10229-5</a>.","short":"M. Konopik, R. T. Sato Martín de Almagro, S. Maslovskaya, S. Ober-Blöbaum, S. Leyendecker, Journal of Nonlinear Science 36 (2025).","ama":"Konopik M, T. Sato Martín de Almagro R, Maslovskaya S, Ober-Blöbaum S, Leyendecker S. Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term. <i>Journal of Nonlinear Science</i>. 2025;36(11). doi:<a href=\"https://doi.org/10.1007/s00332-025-10229-5\">10.1007/s00332-025-10229-5</a>","chicago":"Konopik, Michael, Rodrigo T. Sato Martín de Almagro, Sofya Maslovskaya, Sina Ober-Blöbaum, and Sigrid Leyendecker. “Variational Integrators for a New Lagrangian Approach to Control Affine Systems with a Quadratic Lagrange Term.” <i>Journal of Nonlinear Science</i> 36, no. 11 (2025). <a href=\"https://doi.org/10.1007/s00332-025-10229-5\">https://doi.org/10.1007/s00332-025-10229-5</a>.","bibtex":"@article{Konopik_T. Sato Martín de Almagro_Maslovskaya_Ober-Blöbaum_Leyendecker_2025, title={Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term}, volume={36}, DOI={<a href=\"https://doi.org/10.1007/s00332-025-10229-5\">10.1007/s00332-025-10229-5</a>}, number={11}, journal={Journal of Nonlinear Science}, author={Konopik, Michael and T. Sato Martín de Almagro, Rodrigo and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Leyendecker, Sigrid}, year={2025} }"},"issue":"11","publication":"Journal of Nonlinear Science","department":[{"_id":"636"}],"type":"journal_article","date_created":"2025-05-05T09:35:31Z"},{"user_id":"87909","doi":"10.1088/1361-6544/ae1d08","volume":38,"language":[{"iso":"eng"}],"_id":"59799","date_updated":"2026-01-06T18:24:40Z","intvolume":"        38","title":"A new Lagrangian approach to optimal control of second-order systems","status":"public","year":"2025","author":[{"first_name":"Michael","last_name":"Konopik","full_name":"Konopik, Michael"},{"first_name":"Sigrid","last_name":"Leyendecker","full_name":"Leyendecker, Sigrid"},{"last_name":"Maslovskaya","first_name":"Sofya","full_name":"Maslovskaya, Sofya","id":"87909"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Rodrigo","last_name":"T. Sato Martín de Almagro","full_name":"T. Sato Martín de Almagro, Rodrigo"}],"type":"journal_article","department":[{"_id":"636"}],"date_created":"2025-05-05T09:37:50Z","issue":"11","publication":"Nonlinearity","citation":{"ama":"Konopik M, Leyendecker S, Maslovskaya S, Ober-Blöbaum S, T. Sato Martín de Almagro R. A new Lagrangian approach to optimal control of second-order systems. <i>Nonlinearity</i>. 2025;38(11). doi:<a href=\"https://doi.org/10.1088/1361-6544/ae1d08\">10.1088/1361-6544/ae1d08</a>","short":"M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R. T. Sato Martín de Almagro, Nonlinearity 38 (2025).","chicago":"Konopik, Michael, Sigrid Leyendecker, Sofya Maslovskaya, Sina Ober-Blöbaum, and Rodrigo T. Sato Martín de Almagro. “A New Lagrangian Approach to Optimal Control of Second-Order Systems.” <i>Nonlinearity</i> 38, no. 11 (2025). <a href=\"https://doi.org/10.1088/1361-6544/ae1d08\">https://doi.org/10.1088/1361-6544/ae1d08</a>.","bibtex":"@article{Konopik_Leyendecker_Maslovskaya_Ober-Blöbaum_T. Sato Martín de Almagro_2025, title={A new Lagrangian approach to optimal control of second-order systems}, volume={38}, DOI={<a href=\"https://doi.org/10.1088/1361-6544/ae1d08\">10.1088/1361-6544/ae1d08</a>}, number={11}, journal={Nonlinearity}, author={Konopik, Michael and Leyendecker, Sigrid and Maslovskaya, Sofya and Ober-Blöbaum, Sina and T. Sato Martín de Almagro, Rodrigo}, year={2025} }","mla":"Konopik, Michael, et al. “A New Lagrangian Approach to Optimal Control of Second-Order Systems.” <i>Nonlinearity</i>, vol. 38, no. 11, 2025, doi:<a href=\"https://doi.org/10.1088/1361-6544/ae1d08\">10.1088/1361-6544/ae1d08</a>.","apa":"Konopik, M., Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., &#38; T. Sato Martín de Almagro, R. (2025). A new Lagrangian approach to optimal control of second-order systems. <i>Nonlinearity</i>, <i>38</i>(11). <a href=\"https://doi.org/10.1088/1361-6544/ae1d08\">https://doi.org/10.1088/1361-6544/ae1d08</a>","ieee":"M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, and R. T. Sato Martín de Almagro, “A new Lagrangian approach to optimal control of second-order systems,” <i>Nonlinearity</i>, vol. 38, no. 11, 2025, doi: <a href=\"https://doi.org/10.1088/1361-6544/ae1d08\">10.1088/1361-6544/ae1d08</a>."}},{"status":"public","conference":{"end_date":"2024-12-13","name":"28th International Conference on Principles of Distributed Systems (OPODIS 2024)","start_date":"2024-12-11","location":"Lucca, Italy"},"user_id":"97359","editor":[{"first_name":"Silvia","last_name":"Bonomi","full_name":"Bonomi, Silvia"},{"full_name":"Galletta, Letterio","first_name":"Letterio","last_name":"Galletta"},{"first_name":" Etienne","last_name":"Rivière","full_name":"Rivière,  Etienne"},{"full_name":"Schiavoni,  Valerio","last_name":"Schiavoni","first_name":" Valerio"}],"volume":324,"_id":"56298","publisher":"Schloss Dagstuhl -- Leibniz-Zentrum für Informatik","project":[{"_id":"106","grant_number":"453112019","name":"Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme"}],"citation":{"ama":"Gerlach R, von der Gracht S, Hahn C, Harbig J, Kling P. Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility. In: Bonomi S, Galletta L, Rivière  Etienne, Schiavoni  Valerio, eds. <i>28th International Conference on Principles of Distributed Systems (OPODIS 2024)</i>. Vol 324. Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl -- Leibniz-Zentrum für Informatik; 2025. doi:<a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">10.4230/LIPIcs.OPODIS.2024.13</a>","bibtex":"@inproceedings{Gerlach_von der Gracht_Hahn_Harbig_Kling_2025, series={Leibniz International Proceedings in Informatics (LIPIcs)}, title={Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility}, volume={324}, DOI={<a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">10.4230/LIPIcs.OPODIS.2024.13</a>}, booktitle={28th International Conference on Principles of Distributed Systems (OPODIS 2024)}, publisher={Schloss Dagstuhl -- Leibniz-Zentrum für Informatik}, author={Gerlach, Raphael and von der Gracht, Sören and Hahn, Christopher and Harbig, Jonas and Kling, Peter}, editor={Bonomi, Silvia and Galletta, Letterio and Rivière,  Etienne and Schiavoni,  Valerio}, year={2025}, collection={Leibniz International Proceedings in Informatics (LIPIcs)} }","mla":"Gerlach, Raphael, et al. “Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility.” <i>28th International Conference on Principles of Distributed Systems (OPODIS 2024)</i>, edited by Silvia Bonomi et al., vol. 324, Schloss Dagstuhl -- Leibniz-Zentrum für Informatik, 2025, doi:<a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">10.4230/LIPIcs.OPODIS.2024.13</a>.","short":"R. Gerlach, S. von der Gracht, C. Hahn, J. Harbig, P. Kling, in: S. Bonomi, L. Galletta,  Etienne Rivière,  Valerio Schiavoni (Eds.), 28th International Conference on Principles of Distributed Systems (OPODIS 2024), Schloss Dagstuhl -- Leibniz-Zentrum für Informatik, 2025.","chicago":"Gerlach, Raphael, Sören von der Gracht, Christopher Hahn, Jonas Harbig, and Peter Kling. “Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility.” In <i>28th International Conference on Principles of Distributed Systems (OPODIS 2024)</i>, edited by Silvia Bonomi, Letterio Galletta,  Etienne Rivière, and  Valerio Schiavoni, Vol. 324. Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl -- Leibniz-Zentrum für Informatik, 2025. <a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">https://doi.org/10.4230/LIPIcs.OPODIS.2024.13</a>.","apa":"Gerlach, R., von der Gracht, S., Hahn, C., Harbig, J., &#38; Kling, P. (2025). Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility. In S. Bonomi, L. Galletta,  Etienne Rivière, &#38;  Valerio Schiavoni (Eds.), <i>28th International Conference on Principles of Distributed Systems (OPODIS 2024)</i> (Vol. 324). Schloss Dagstuhl -- Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">https://doi.org/10.4230/LIPIcs.OPODIS.2024.13</a>","ieee":"R. Gerlach, S. von der Gracht, C. Hahn, J. Harbig, and P. Kling, “Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility,” in <i>28th International Conference on Principles of Distributed Systems (OPODIS 2024)</i>, Lucca, Italy, 2025, vol. 324, doi: <a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">10.4230/LIPIcs.OPODIS.2024.13</a>."},"oa":"1","external_id":{"arxiv":["2409.19277"]},"date_updated":"2025-01-09T11:39:19Z","publication_status":"published","intvolume":"       324","title":"Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility","year":"2025","author":[{"id":"32655","first_name":"Raphael","orcid":"0009-0002-4750-2051","last_name":"Gerlach","full_name":"Gerlach, Raphael"},{"id":"97359","full_name":"von der Gracht, Sören","orcid":"0000-0002-8054-2058","first_name":"Sören","last_name":"von der Gracht"},{"full_name":"Hahn, Christopher","first_name":"Christopher","last_name":"Hahn"},{"full_name":"Harbig, Jonas","first_name":"Jonas","last_name":"Harbig","id":"47213"},{"full_name":"Kling, Peter","last_name":"Kling","first_name":"Peter"}],"publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-360-7"]},"doi":"10.4230/LIPIcs.OPODIS.2024.13","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2409.19277"}],"series_title":"Leibniz International Proceedings in Informatics (LIPIcs)","language":[{"iso":"eng"}],"abstract":[{"text":"In the general pattern formation (GPF) problem, a swarm of simple autonomous,\r\ndisoriented robots must form a given pattern. The robots' simplicity imply a\r\nstrong limitation: When the initial configuration is rotationally symmetric,\r\nonly patterns with a similar symmetry can be formed [Yamashita, Suzyuki; TCS\r\n2010]. The only known algorithm to form large patterns with limited visibility\r\nand without memory requires the robots to start in a near-gathering (a swarm of\r\nconstant diameter) [Hahn et al.; SAND 2024]. However, not only do we not know\r\nany near-gathering algorithm guaranteed to preserve symmetry but most natural\r\ngathering strategies trivially increase symmetries [Castenow et al.; OPODIS\r\n2022].\r\n  Thus, we study near-gathering without changing the swarm's rotational\r\nsymmetry for disoriented, oblivious robots with limited visibility (the\r\nOBLOT-model, see [Flocchini et al.; 2019]). We introduce a technique based on\r\nthe theory of dynamical systems to analyze how a given algorithm affects\r\nsymmetry and provide sufficient conditions for symmetry preservation. Until\r\nnow, it was unknown whether the considered OBLOT-model allows for any\r\nnon-trivial algorithm that always preserves symmetry. Our first result shows\r\nthat a variant of Go-to-the-Average always preserves symmetry but may sometimes\r\nlead to multiple, unconnected near-gathering clusters. Our second result is a\r\nsymmetry-preserving near-gathering algorithm that works on swarms with a convex\r\nboundary (the outer boundary of the unit disc graph) and without holes (circles\r\nof diameter 1 inside the boundary without any robots).","lang":"eng"}],"publication":"28th International Conference on Principles of Distributed Systems (OPODIS 2024)","type":"conference","keyword":["Swarm Algorithm","Swarm Robots","Distributed Algorithm","Pattern Formation","Limited Visibility","Oblivious"],"department":[{"_id":"101"}],"date_created":"2024-10-01T13:29:43Z"},{"date_created":"2025-02-07T08:27:10Z","type":"journal_article","department":[{"_id":"841"}],"publication":"arXiv","citation":{"ieee":"N. Bullerjahn, “Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions,” <i>arXiv</i>, 2025, doi: <a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">10.48550/ARXIV.2502.03847</a>.","mla":"Bullerjahn, Nils. “Error Estimates for Full Discretization by an Almost Mass Conservation Technique for Cahn--Hilliard Systems with Dynamic Boundary Conditions.” <i>ArXiv</i>, 2025, doi:<a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">10.48550/ARXIV.2502.03847</a>.","apa":"Bullerjahn, N. (2025). Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions. <i>ArXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">https://doi.org/10.48550/ARXIV.2502.03847</a>","bibtex":"@article{Bullerjahn_2025, title={Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions}, DOI={<a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">10.48550/ARXIV.2502.03847</a>}, journal={arXiv}, author={Bullerjahn, Nils}, year={2025} }","short":"N. Bullerjahn, ArXiv (2025).","ama":"Bullerjahn N. Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions. <i>arXiv</i>. Published online 2025. doi:<a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">10.48550/ARXIV.2502.03847</a>","chicago":"Bullerjahn, Nils. “Error Estimates for Full Discretization by an Almost Mass Conservation Technique for Cahn--Hilliard Systems with Dynamic Boundary Conditions.” <i>ArXiv</i>, 2025. <a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">https://doi.org/10.48550/ARXIV.2502.03847</a>."},"language":[{"iso":"eng"}],"_id":"58532","doi":"10.48550/ARXIV.2502.03847","user_id":"103797","status":"public","year":"2025","title":"Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions","author":[{"id":"103797","last_name":"Bullerjahn","orcid":"https://orcid.org/0009-0003-8460-1574","first_name":"Nils","full_name":"Bullerjahn, Nils"}],"date_updated":"2025-02-07T08:28:48Z"},{"author":[{"full_name":"Kopylov, Denis","first_name":"Denis","last_name":"Kopylov","id":"98502"},{"id":"85279","last_name":"Offen","orcid":"0000-0002-5940-8057","first_name":"Christian","full_name":"Offen, Christian"},{"full_name":"Ares, Laura","first_name":"Laura","last_name":"Ares"},{"id":"95394","full_name":"Wembe Moafo, Boris Edgar","first_name":"Boris Edgar","last_name":"Wembe Moafo"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494"},{"id":"344","full_name":"Meier, Torsten","last_name":"Meier","first_name":"Torsten","orcid":"0000-0001-8864-2072"},{"id":"60286","first_name":"Polina","last_name":"Sharapova","full_name":"Sharapova, Polina"},{"full_name":"Sperling, Jan","last_name":"Sperling","orcid":"0000-0002-5844-3205","first_name":"Jan","id":"75127"}],"year":"2025","status":"public","title":"Multiphoton, multimode state classification for nonlinear optical circuits ","date_updated":"2025-02-10T08:36:12Z","publication_status":"submitted","_id":"58544","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2502.05123","open_access":"1"}],"user_id":"85279","citation":{"chicago":"Kopylov, Denis, Christian Offen, Laura Ares, Boris Edgar Wembe Moafo, Sina Ober-Blöbaum, Torsten Meier, Polina Sharapova, and Jan Sperling. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits ,” n.d.","short":"D. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier, P. Sharapova, J. Sperling, (n.d.).","ieee":"D. Kopylov <i>et al.</i>, “Multiphoton, multimode state classification for nonlinear optical circuits .” .","apa":"Kopylov, D., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S., Meier, T., Sharapova, P., &#38; Sperling, J. (n.d.). <i>Multiphoton, multimode state classification for nonlinear optical circuits </i>.","bibtex":"@article{Kopylov_Offen_Ares_Wembe Moafo_Ober-Blöbaum_Meier_Sharapova_Sperling, title={Multiphoton, multimode state classification for nonlinear optical circuits }, author={Kopylov, Denis and Offen, Christian and Ares, Laura and Wembe Moafo, Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova, Polina and Sperling, Jan} }","ama":"Kopylov D, Offen C, Ares L, et al. Multiphoton, multimode state classification for nonlinear optical circuits .","mla":"Kopylov, Denis, et al. <i>Multiphoton, Multimode State Classification for Nonlinear Optical Circuits </i>."},"abstract":[{"lang":"eng","text":"We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which being in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes. "}],"date_created":"2025-02-10T08:26:45Z","external_id":{"arxiv":["2502.05123"]},"oa":"1","department":[{"_id":"623"},{"_id":"15"},{"_id":"636"}],"type":"preprint"},{"external_id":{"arxiv":["2503.07576"]},"oa":"1","citation":{"apa":"Gerlach, R., &#38; von der Gracht, S. (2025). Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems. In <i>arXiv:2503.07576</i>.","mla":"Gerlach, Raphael, and Sören von der Gracht. “Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems.” <i>ArXiv:2503.07576</i>, 2025.","ieee":"R. Gerlach and S. von der Gracht, “Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems,” <i>arXiv:2503.07576</i>. 2025.","chicago":"Gerlach, Raphael, and Sören von der Gracht. “Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems.” <i>ArXiv:2503.07576</i>, 2025.","ama":"Gerlach R, von der Gracht S. Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems. <i>arXiv:250307576</i>. Published online 2025.","short":"R. Gerlach, S. von der Gracht, ArXiv:2503.07576 (2025).","bibtex":"@article{Gerlach_von der Gracht_2025, title={Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems}, journal={arXiv:2503.07576}, author={Gerlach, Raphael and von der Gracht, Sören}, year={2025} }"},"file_date_updated":"2025-03-11T08:27:32Z","project":[{"grant_number":"453112019","_id":"106","name":"Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme"}],"_id":"58953","page":"23","user_id":"97359","ddc":["004"],"status":"public","has_accepted_license":"1","date_created":"2025-03-11T08:21:05Z","file":[{"file_id":"58954","content_type":"application/pdf","relation":"main_file","date_updated":"2025-03-11T08:27:32Z","file_name":"Analyzing_Symmetries_of_Swarms_of_Mobile_Robots_Using_Equivariant_Dynamical_Systems.pdf","file_size":812198,"access_level":"open_access","date_created":"2025-03-11T08:27:32Z","creator":"svdg"}],"department":[{"_id":"101"}],"type":"preprint","keyword":["dynamical systems","coupled systems","distributed computing","robot swarms","autonomous mobile robots","symmetry","equivariant dynamics"],"publication":"arXiv:2503.07576","abstract":[{"lang":"eng","text":"In this article, we investigate symmetry properties of distributed systems of mobile robots. We consider a swarm of n robots in the OBLOT model and analyze their collective Fsync dynamics using of equivariant dynamical systems theory. To this end, we show that the corresponding evolution function commutes with rotational and reflective transformations of R^2. These form a group that is isomorphic to O(2) x S_n, the product group of the orthogonal group and the permutation on n elements. The theory of equivariant dynamical systems is used to deduce a hierarchy along which symmetries of a robot swarm can potentially increase following an arbitrary protocol. By decoupling the Look phase from the Compute and Move phases in the mathematical description of an LCM cycle, this hierarchy can be characterized in terms of automorphisms of connectivity graphs. In particular, we find all possible types of symmetry increase, if the decoupled Compute and Move phase is invertible. Finally, we apply our results to protocols which induce state-dependent linear dynamics, where the reduced system consisting of only the Compute and Move phase is linear."}],"language":[{"iso":"eng"}],"author":[{"id":"32655","last_name":"Gerlach","orcid":"0009-0002-4750-2051","first_name":"Raphael","full_name":"Gerlach, Raphael"},{"id":"97359","full_name":"von der Gracht, Sören","first_name":"Sören","last_name":"von der Gracht","orcid":"0000-0002-8054-2058"}],"title":"Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems","year":"2025","date_updated":"2025-03-11T08:53:02Z"},{"date_created":"2025-03-27T09:46:34Z","department":[{"_id":"542"}],"type":"journal_article","publication":"Combinatorica","issue":"2","abstract":[{"lang":"eng","text":"An r-regular graph is an r-graph, if every odd set of vertices is connected to its complement by at least r edges. Let G and H be r-graphs. An H-coloring of G is a mapping such that each r adjacent edges of G are mapped to r adjacent edges of H. For every , let be an inclusion-wise minimal set of connected r-graphs, such that for every connected r-graph G there is an which colors G. The Petersen Coloring Conjecture states that consists of the Petersen graph P. We show that if true, then this is a very exclusive situation. Our main result is that either or is an infinite set and if , then is an infinite set. In particular, for all , is unique. We first characterize and then prove that if contains more than one element, then it is an infinite set. To obtain our main result we show that contains the smallest r-graphs of class 2 and the smallest poorly matchable r-graphs, and we determine the smallest r-graphs of class 2."}],"language":[{"iso":"eng"}],"article_number":"16","doi":"10.1007/s00493-025-00144-4","publication_identifier":{"issn":["0209-9683","1439-6912"]},"author":[{"full_name":"Ma, Yulai","first_name":"Yulai","last_name":"Ma"},{"last_name":"Mattiolo","first_name":"Davide","full_name":"Mattiolo, Davide"},{"full_name":"Steffen, Eckhard","orcid":"0000-0002-9808-7401","last_name":"Steffen","first_name":"Eckhard","id":"15548"},{"first_name":"Isaak H.","last_name":"Wolf","full_name":"Wolf, Isaak H."}],"year":"2025","title":"Sets of r-Graphs that Color All r-Graphs","intvolume":"        45","date_updated":"2025-03-27T09:48:48Z","publication_status":"published","citation":{"ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Sets of r-Graphs that Color All r-Graphs. <i>Combinatorica</i>. 2025;45(2). doi:<a href=\"https://doi.org/10.1007/s00493-025-00144-4\">10.1007/s00493-025-00144-4</a>","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2025, title={Sets of r-Graphs that Color All r-Graphs}, volume={45}, DOI={<a href=\"https://doi.org/10.1007/s00493-025-00144-4\">10.1007/s00493-025-00144-4</a>}, number={216}, journal={Combinatorica}, publisher={Springer Science and Business Media LLC}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak H.}, year={2025} }","mla":"Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” <i>Combinatorica</i>, vol. 45, no. 2, 16, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s00493-025-00144-4\">10.1007/s00493-025-00144-4</a>.","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 45 (2025).","chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak H. Wolf. “Sets of R-Graphs That Color All r-Graphs.” <i>Combinatorica</i> 45, no. 2 (2025). <a href=\"https://doi.org/10.1007/s00493-025-00144-4\">https://doi.org/10.1007/s00493-025-00144-4</a>.","apa":"Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2025). Sets of r-Graphs that Color All r-Graphs. <i>Combinatorica</i>, <i>45</i>(2), Article 16. <a href=\"https://doi.org/10.1007/s00493-025-00144-4\">https://doi.org/10.1007/s00493-025-00144-4</a>","ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Sets of r-Graphs that Color All r-Graphs,” <i>Combinatorica</i>, vol. 45, no. 2, Art. no. 16, 2025, doi: <a href=\"https://doi.org/10.1007/s00493-025-00144-4\">10.1007/s00493-025-00144-4</a>."},"publisher":"Springer Science and Business Media LLC","_id":"59169","volume":45,"user_id":"15540","status":"public"},{"file_date_updated":"2025-05-02T13:20:31Z","citation":{"short":"C. Offen, Mathematics of Computation (2025).","chicago":"Offen, Christian. “Machine Learning of Continuous and Discrete Variational ODEs with Convergence Guarantee and Uncertainty Quantification.” <i>Mathematics of Computation</i>, 2025. <a href=\"https://doi.org/10.1090/mcom/4120\">https://doi.org/10.1090/mcom/4120</a>.","apa":"Offen, C. (2025). Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification. <i>Mathematics of Computation</i>. <a href=\"https://doi.org/10.1090/mcom/4120\">https://doi.org/10.1090/mcom/4120</a>","ieee":"C. Offen, “Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification,” <i>Mathematics of Computation</i>, 2025, doi: <a href=\"https://doi.org/10.1090/mcom/4120\">10.1090/mcom/4120</a>.","ama":"Offen C. Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification. <i>Mathematics of Computation</i>. Published online 2025. doi:<a href=\"https://doi.org/10.1090/mcom/4120\">10.1090/mcom/4120</a>","bibtex":"@article{Offen_2025, title={Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification}, DOI={<a href=\"https://doi.org/10.1090/mcom/4120\">10.1090/mcom/4120</a>}, journal={Mathematics of Computation}, publisher={American Mathematical Society}, author={Offen, Christian}, year={2025} }","mla":"Offen, Christian. “Machine Learning of Continuous and Discrete Variational ODEs with Convergence Guarantee and Uncertainty Quantification.” <i>Mathematics of Computation</i>, American Mathematical Society, 2025, doi:<a href=\"https://doi.org/10.1090/mcom/4120\">10.1090/mcom/4120</a>."},"quality_controlled":"1","project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"external_id":{"arxiv":["arXiv:2404.19626"]},"oa":"1","status":"public","has_accepted_license":"1","publisher":"American Mathematical Society","_id":"53805","ddc":["510"],"user_id":"85279","publication":"Mathematics of Computation","abstract":[{"text":"The article introduces a method to learn dynamical systems that are governed by Euler–Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore, structure preserving by design. A rigorous proof of convergence as the distance between observation data points converges to zero and lower bounds for convergence rates are provided. Next to convergence guarantees, the method allows for quantification of model uncertainty, which can provide a basis of adaptive sampling techniques. We provide efficient uncertainty quantification of any observable that is linear in the Lagrangian, including of Hamiltonian functions (energy) and symplectic structures, which is of interest in the context of system identification. The article overcomes major practical and theoretical difficulties related to the ill-posedness of the identification task of (discrete) Lagrangians through a careful design of geometric regularisation strategies and through an exploit of a relation to convex minimisation problems in reproducing kernel Hilbert spaces.","lang":"eng"}],"related_material":{"link":[{"description":"GitHub","relation":"software","url":"https://github.com/Christian-Offen/Lagrangian_GP"}]},"file":[{"date_updated":"2025-05-02T13:20:31Z","relation":"main_file","file_size":1819189,"access_level":"open_access","file_name":"L_Collocation_ODE_mcom-l-template.pdf","title":"Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification ","content_type":"application/pdf","file_id":"59759","creator":"coffen","description":"The article introduces a method to learn dynamical systems that\nare governed by Euler–Lagrange equations from data. The method is based on\nGaussian process regression and identifies continuous or discrete Lagrangians\nand is, therefore, structure preserving by design. A rigorous proof of con-\nvergence as the distance between observation data points converges to zero\nand lower bounds for convergence rates are provided. Next to convergence\nguarantees, the method allows for quantification of model uncertainty, which\ncan provide a basis of adaptive sampling techniques. We provide efficient uncertainty quantification of any observable that is linear in the Lagrangian,\nincluding of Hamiltonian functions (energy) and symplectic structures, which\nis of interest in the context of system identification. The article overcomes\nmajor practical and theoretical difficulties related to the ill-posedness of the\nidentification task of (discrete) Lagrangians through a careful design of geometric regularisation strategies and through an exploit of a relation to convex\nminimisation problems in reproducing kernel Hilbert spaces.","date_created":"2025-05-02T13:20:31Z"}],"date_created":"2024-04-30T16:04:40Z","type":"journal_article","department":[{"_id":"636"}],"year":"2025","title":"Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification","author":[{"id":"85279","first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","full_name":"Offen, Christian"}],"date_updated":"2025-06-29T13:03:55Z","publication_status":"epub_ahead","article_type":"original","language":[{"iso":"eng"}],"doi":"10.1090/mcom/4120"},{"citation":{"mla":"Dalfó, C., et al. “On Token Signed Graphs.” <i>Journal of Algebraic Combinatorics</i>, vol. 62, no. 1, 7, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s10801-025-01416-4\">10.1007/s10801-025-01416-4</a>.","ama":"Dalfó C, Fiol MA, Steffen E. On token signed graphs. <i>Journal of Algebraic Combinatorics</i>. 2025;62(1). doi:<a href=\"https://doi.org/10.1007/s10801-025-01416-4\">10.1007/s10801-025-01416-4</a>","bibtex":"@article{Dalfó_Fiol_Steffen_2025, title={On token signed graphs}, volume={62}, DOI={<a href=\"https://doi.org/10.1007/s10801-025-01416-4\">10.1007/s10801-025-01416-4</a>}, number={17}, journal={Journal of Algebraic Combinatorics}, publisher={Springer Science and Business Media LLC}, author={Dalfó, C. and Fiol, M. A. and Steffen, Eckhard}, year={2025} }","apa":"Dalfó, C., Fiol, M. A., &#38; Steffen, E. (2025). On token signed graphs. <i>Journal of Algebraic Combinatorics</i>, <i>62</i>(1), Article 7. <a href=\"https://doi.org/10.1007/s10801-025-01416-4\">https://doi.org/10.1007/s10801-025-01416-4</a>","ieee":"C. Dalfó, M. A. Fiol, and E. Steffen, “On token signed graphs,” <i>Journal of Algebraic Combinatorics</i>, vol. 62, no. 1, Art. no. 7, 2025, doi: <a href=\"https://doi.org/10.1007/s10801-025-01416-4\">10.1007/s10801-025-01416-4</a>.","short":"C. Dalfó, M.A. Fiol, E. Steffen, Journal of Algebraic Combinatorics 62 (2025).","chicago":"Dalfó, C., M. A. Fiol, and Eckhard Steffen. “On Token Signed Graphs.” <i>Journal of Algebraic Combinatorics</i> 62, no. 1 (2025). <a href=\"https://doi.org/10.1007/s10801-025-01416-4\">https://doi.org/10.1007/s10801-025-01416-4</a>."},"status":"public","publisher":"Springer Science and Business Media LLC","_id":"61042","volume":62,"user_id":"15540","publication":"Journal of Algebraic Combinatorics","issue":"1","abstract":[{"text":"We introduce the concept of a k-token signed graph and study some of its combinatorial and algebraic properties. We prove that two switching isomorphic signed graphs have switching isomorphic token graphs. Moreover, we show that the Laplacian spectrum of a balanced signed graph is contained in the Laplacian spectra of its k-token signed graph. Besides, we introduce and study the unbalance level of a signed graph, which is a new parameter that measures how far a signed graph is from being balanced. Moreover, we study the relation between the frustration index and the unbalance level of signed graphs and their token signed graphs.","lang":"eng"}],"date_created":"2025-08-28T07:50:03Z","department":[{"_id":"542"}],"type":"journal_article","author":[{"full_name":"Dalfó, C.","first_name":"C.","last_name":"Dalfó"},{"first_name":"M. A.","last_name":"Fiol","full_name":"Fiol, M. A."},{"id":"15548","last_name":"Steffen","first_name":"Eckhard","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard"}],"publication_identifier":{"issn":["0925-9899","1572-9192"]},"year":"2025","title":"On token signed graphs","intvolume":"        62","publication_status":"published","date_updated":"2025-08-28T07:57:27Z","language":[{"iso":"eng"}],"article_number":"7","doi":"10.1007/s10801-025-01416-4"},{"date_created":"2024-02-07T07:23:23Z","department":[{"_id":"101"}],"type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics","Control and Optimization"],"citation":{"bibtex":"@article{Gebken_2024, title={A note on the convergence of deterministic gradient sampling in nonsmooth optimization}, DOI={<a href=\"https://doi.org/10.1007/s10589-024-00552-0\">10.1007/s10589-024-00552-0</a>}, journal={Computational Optimization and Applications}, publisher={Springer Science and Business Media LLC}, author={Gebken, Bennet}, year={2024} }","ama":"Gebken B. A note on the convergence of deterministic gradient sampling in nonsmooth optimization. <i>Computational Optimization and Applications</i>. Published online 2024. doi:<a href=\"https://doi.org/10.1007/s10589-024-00552-0\">10.1007/s10589-024-00552-0</a>","mla":"Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling in Nonsmooth Optimization.” <i>Computational Optimization and Applications</i>, Springer Science and Business Media LLC, 2024, doi:<a href=\"https://doi.org/10.1007/s10589-024-00552-0\">10.1007/s10589-024-00552-0</a>.","short":"B. Gebken, Computational Optimization and Applications (2024).","chicago":"Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling in Nonsmooth Optimization.” <i>Computational Optimization and Applications</i>, 2024. <a href=\"https://doi.org/10.1007/s10589-024-00552-0\">https://doi.org/10.1007/s10589-024-00552-0</a>.","ieee":"B. Gebken, “A note on the convergence of deterministic gradient sampling in nonsmooth optimization,” <i>Computational Optimization and Applications</i>, 2024, doi: <a href=\"https://doi.org/10.1007/s10589-024-00552-0\">10.1007/s10589-024-00552-0</a>.","apa":"Gebken, B. (2024). A note on the convergence of deterministic gradient sampling in nonsmooth optimization. <i>Computational Optimization and Applications</i>. <a href=\"https://doi.org/10.1007/s10589-024-00552-0\">https://doi.org/10.1007/s10589-024-00552-0</a>"},"publication":"Computational Optimization and Applications","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Approximation 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.</jats:p>","lang":"eng"}],"_id":"51208","publisher":"Springer Science and Business Media LLC","language":[{"iso":"eng"}],"user_id":"32643","doi":"10.1007/s10589-024-00552-0","publication_identifier":{"issn":["0926-6003","1573-2894"]},"author":[{"full_name":"Gebken, Bennet","first_name":"Bennet","last_name":"Gebken","id":"32643"}],"status":"public","year":"2024","title":"A note on the convergence of deterministic gradient sampling in nonsmooth optimization","publication_status":"published","date_updated":"2024-02-08T08:05:54Z"},{"date_created":"2023-07-12T06:35:58Z","type":"journal_article","oa":"1","department":[{"_id":"101"},{"_id":"655"}],"publication":"Journal of Optimization Theory and Applications","citation":{"mla":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” <i>Journal of Optimization Theory and Applications</i>, Springer, 2024, doi:<a href=\"https://doi.org/10.1007/s10957-024-02389-3\">10.1007/s10957-024-02389-3</a>.","ama":"Sonntag K, Peitz S. Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems. <i>Journal of Optimization Theory and Applications</i>. Published online 2024. doi:<a href=\"https://doi.org/10.1007/s10957-024-02389-3\">10.1007/s10957-024-02389-3</a>","bibtex":"@article{Sonntag_Peitz_2024, title={Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems}, DOI={<a href=\"https://doi.org/10.1007/s10957-024-02389-3\">10.1007/s10957-024-02389-3</a>}, journal={Journal of Optimization Theory and Applications}, publisher={Springer}, author={Sonntag, Konstantin and Peitz, Sebastian}, year={2024} }","apa":"Sonntag, K., &#38; Peitz, S. (2024). Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems. <i>Journal of Optimization Theory and Applications</i>. <a href=\"https://doi.org/10.1007/s10957-024-02389-3\">https://doi.org/10.1007/s10957-024-02389-3</a>","ieee":"K. Sonntag and S. Peitz, “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems,” <i>Journal of Optimization Theory and Applications</i>, 2024, doi: <a href=\"https://doi.org/10.1007/s10957-024-02389-3\">10.1007/s10957-024-02389-3</a>.","chicago":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” <i>Journal of Optimization Theory and Applications</i>, 2024. <a href=\"https://doi.org/10.1007/s10957-024-02389-3\">https://doi.org/10.1007/s10957-024-02389-3</a>.","short":"K. Sonntag, S. Peitz, Journal of Optimization Theory and Applications (2024)."},"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"}],"main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10957-024-02389-3.pdf","open_access":"1"}],"_id":"46019","language":[{"iso":"eng"}],"publisher":"Springer","doi":"10.1007/s10957-024-02389-3","user_id":"56399","year":"2024","status":"public","title":"Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems","author":[{"id":"56399","orcid":"https://orcid.org/0000-0003-3384-3496","first_name":"Konstantin","last_name":"Sonntag","full_name":"Sonntag, Konstantin"},{"full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian","id":"47427"}],"date_updated":"2024-02-21T10:13:33Z","publication_status":"published"},{"external_id":{"arxiv":["\t2402.06376"]},"date_created":"2024-02-13T09:35:26Z","type":"preprint","oa":"1","department":[{"_id":"101"},{"_id":"655"}],"publication":"arXiv:2402.06376","citation":{"ieee":"K. Sonntag, B. Gebken, G. Müller, S. Peitz, and S. Volkwein, “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces,” <i>arXiv:2402.06376</i>. 2024.","apa":"Sonntag, K., Gebken, B., Müller, G., Peitz, S., &#38; Volkwein, S. (2024). A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces. In <i>arXiv:2402.06376</i>.","short":"K. Sonntag, B. Gebken, G. Müller, S. Peitz, S. Volkwein, ArXiv:2402.06376 (2024).","chicago":"Sonntag, Konstantin, Bennet Gebken, Georg Müller, Sebastian Peitz, and Stefan Volkwein. “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.” <i>ArXiv:2402.06376</i>, 2024.","mla":"Sonntag, Konstantin, et al. “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.” <i>ArXiv:2402.06376</i>, 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} }","ama":"Sonntag K, Gebken B, Müller G, Peitz S, Volkwein S. A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces. <i>arXiv:240206376</i>. Published online 2024."},"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."}],"main_file_link":[{"url":"https://arxiv.org/abs/2402.06376","open_access":"1"}],"_id":"51334","language":[{"iso":"eng"}],"user_id":"56399","title":"A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces","year":"2024","status":"public","author":[{"id":"56399","last_name":"Sonntag","first_name":"Konstantin","orcid":"https://orcid.org/0000-0003-3384-3496","full_name":"Sonntag, Konstantin"},{"first_name":"Bennet","last_name":"Gebken","full_name":"Gebken, Bennet","id":"32643"},{"first_name":"Georg","last_name":"Müller","full_name":"Müller, Georg"},{"id":"47427","first_name":"Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian"},{"last_name":"Volkwein","first_name":"Stefan","full_name":"Volkwein, Stefan"}],"date_updated":"2024-02-21T10:21:03Z","has_accepted_license":"1"},{"has_accepted_license":"1","status":"public","user_id":"97359","ddc":["510"],"volume":12,"_id":"52726","publisher":"Oxford University Press (OUP)","file_date_updated":"2024-03-22T09:06:07Z","citation":{"mla":"Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network Dynamical Systems with Higher-Order Interactions.” <i>Journal of Complex Networks</i>, vol. 12, no. 2, Oxford University Press (OUP), 2024, doi:<a href=\"https://doi.org/10.1093/comnet/cnae009\">10.1093/comnet/cnae009</a>.","ama":"Bick C, von der Gracht S. Heteroclinic dynamics in network dynamical systems with higher-order interactions. <i>Journal of Complex Networks</i>. 2024;12(2). doi:<a href=\"https://doi.org/10.1093/comnet/cnae009\">10.1093/comnet/cnae009</a>","bibtex":"@article{Bick_von der Gracht_2024, title={Heteroclinic dynamics in network dynamical systems with higher-order interactions}, volume={12}, DOI={<a href=\"https://doi.org/10.1093/comnet/cnae009\">10.1093/comnet/cnae009</a>}, number={2}, journal={Journal of Complex Networks}, publisher={Oxford University Press (OUP)}, author={Bick, Christian and von der Gracht, Sören}, year={2024} }","apa":"Bick, C., &#38; von der Gracht, S. (2024). Heteroclinic dynamics in network dynamical systems with higher-order interactions. <i>Journal of Complex Networks</i>, <i>12</i>(2). <a href=\"https://doi.org/10.1093/comnet/cnae009\">https://doi.org/10.1093/comnet/cnae009</a>","ieee":"C. Bick and S. von der Gracht, “Heteroclinic dynamics in network dynamical systems with higher-order interactions,” <i>Journal of Complex Networks</i>, vol. 12, no. 2, 2024, doi: <a href=\"https://doi.org/10.1093/comnet/cnae009\">10.1093/comnet/cnae009</a>.","chicago":"Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network Dynamical Systems with Higher-Order Interactions.” <i>Journal of Complex Networks</i> 12, no. 2 (2024). <a href=\"https://doi.org/10.1093/comnet/cnae009\">https://doi.org/10.1093/comnet/cnae009</a>.","short":"C. Bick, S. von der Gracht, Journal of Complex Networks 12 (2024)."},"oa":"1","external_id":{"arxiv":["2309.02006"]},"publication_status":"published","date_updated":"2024-03-22T09:11:53Z","article_type":"original","intvolume":"        12","title":"Heteroclinic dynamics in network dynamical systems with higher-order interactions","year":"2024","author":[{"first_name":"Christian","last_name":"Bick","full_name":"Bick, Christian"},{"last_name":"von der Gracht","first_name":"Sören","orcid":"0000-0002-8054-2058","full_name":"von der Gracht, Sören","id":"97359"}],"publication_identifier":{"issn":["2051-1329"]},"doi":"10.1093/comnet/cnae009","main_file_link":[{"url":"https://academic.oup.com/comnet/article-pdf/12/2/cnae009/56832119/cnae009.pdf","open_access":"1"}],"language":[{"iso":"eng"}],"abstract":[{"text":"Heteroclinic structures organize global features of dynamical systems. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analysed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures.","lang":"eng"}],"issue":"2","publication":"Journal of Complex Networks","keyword":["Applied Mathematics","Computational Mathematics","Control and Optimization","Management Science and Operations Research","Computer Networks and Communications"],"type":"journal_article","department":[{"_id":"101"}],"file":[{"creator":"svdg","date_created":"2024-03-22T09:06:07Z","relation":"main_file","date_updated":"2024-03-22T09:06:07Z","file_name":"heteroclinic-dynamics-in-network-dynamical-systems-with-higher-order-interactions.pdf","access_level":"closed","file_size":649155,"file_id":"52728","success":1,"content_type":"application/pdf"}],"date_created":"2024-03-22T09:04:57Z"},{"date_created":"2023-12-20T10:31:27Z","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics"],"type":"journal_article","department":[{"_id":"542"}],"publication":"Combinatorica","abstract":[{"text":"For 0 ≤ t ≤ r let m(t, r) be the maximum number s such that every t-edge-connected r-graph has s pairwise disjoint perfect matchings. There are only a few values of m(t, r) known, for instance m(3, 3) = m(4, r) = 1, and m(t, r) ≤ r − 2 for all t \u0003 = 5,\r\nand m(t, r) ≤ r − 3 if r is even. We prove that m(2l, r) ≤ 3l − 6 for every l ≥ 3 and r ≥ 2l.","lang":"eng"}],"language":[{"iso":"eng"}],"doi":"10.1007/s00493-023-00078-9","year":"2024","title":"Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs","publication_identifier":{"issn":["0209-9683","1439-6912"]},"author":[{"id":"92748","last_name":"Ma","first_name":"Yulai","full_name":"Ma, Yulai"},{"first_name":"Davide","last_name":"Mattiolo","full_name":"Mattiolo, Davide"},{"full_name":"Steffen, Eckhard","orcid":"0000-0002-9808-7401","last_name":"Steffen","first_name":"Eckhard","id":"15548"},{"id":"88145","full_name":"Wolf, Isaak Hieronymus","first_name":"Isaak Hieronymus","last_name":"Wolf"}],"publication_status":"published","date_updated":"2024-03-22T12:11:35Z","intvolume":"        44","citation":{"apa":"Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2024). Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs. <i>Combinatorica</i>, <i>44</i>, 429–440. <a href=\"https://doi.org/10.1007/s00493-023-00078-9\">https://doi.org/10.1007/s00493-023-00078-9</a>","ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs,” <i>Combinatorica</i>, vol. 44, pp. 429–440, 2024, doi: <a href=\"https://doi.org/10.1007/s00493-023-00078-9\">10.1007/s00493-023-00078-9</a>.","chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.” <i>Combinatorica</i> 44 (2024): 429–40. <a href=\"https://doi.org/10.1007/s00493-023-00078-9\">https://doi.org/10.1007/s00493-023-00078-9</a>.","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 44 (2024) 429–440.","mla":"Ma, Yulai, et al. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.” <i>Combinatorica</i>, vol. 44, Springer Science and Business Media LLC, 2024, pp. 429–40, doi:<a href=\"https://doi.org/10.1007/s00493-023-00078-9\">10.1007/s00493-023-00078-9</a>.","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs. <i>Combinatorica</i>. 2024;44:429-440. doi:<a href=\"https://doi.org/10.1007/s00493-023-00078-9\">10.1007/s00493-023-00078-9</a>","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2024, title={Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs}, volume={44}, DOI={<a href=\"https://doi.org/10.1007/s00493-023-00078-9\">10.1007/s00493-023-00078-9</a>}, journal={Combinatorica}, publisher={Springer Science and Business Media LLC}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2024}, pages={429–440} }"},"page":"429-440","_id":"49905","publisher":"Springer Science and Business Media LLC","user_id":"15540","volume":44,"status":"public"},{"abstract":[{"lang":"eng","text":"In this work, we consider optimal control problems for mechanical systems with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an affine control term. Classically, Pontryagin's maximum principle gives necessary optimality conditions for the optimal control problem. For smooth problems, alternatively, a variational approach based on an augmented objective can be followed. Here, we propose a new Lagrangian approach leading to equivalent necessary optimality conditions in the form of Euler-Lagrange equations. Thus, the differential geometric structure (similar to classical Lagrangian dynamics) can be exploited in the framework of optimal control problems. In particular, the formulation enables the symplectic discretisation of the optimal control problem via variational integrators in a straightforward way."}],"publication":"Journal of Computational Dynamics","issue":"0","department":[{"_id":"636"}],"type":"journal_article","keyword":["Optimal control problem","Lagrangian system","Hamiltonian system","Variations","Pontryagin's maximum principle."],"date_created":"2024-03-28T15:58:02Z","article_type":"original","date_updated":"2024-03-28T16:07:34Z","publication_status":"published","publication_identifier":{"issn":["2158-2491","2158-2505"]},"author":[{"first_name":"Sigrid","last_name":"Leyendecker","full_name":"Leyendecker, Sigrid"},{"last_name":"Maslovskaya","first_name":"Sofya","full_name":"Maslovskaya, Sofya","id":"87909"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494"},{"full_name":"Almagro, Rodrigo T. Sato Martín de","first_name":"Rodrigo T. Sato Martín de","last_name":"Almagro"},{"full_name":"Szemenyei, Flóra Orsolya","last_name":"Szemenyei","first_name":"Flóra Orsolya"}],"year":"2024","title":"A new Lagrangian approach to control affine systems with a quadratic Lagrange term","doi":"10.3934/jcd.2024017","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://www.aimsciences.org/article/doi/10.3934/jcd.2024017"}],"citation":{"ieee":"S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R. T. S. M. de Almagro, and F. O. Szemenyei, “A new Lagrangian approach to control affine systems with a quadratic Lagrange term,” <i>Journal of Computational Dynamics</i>, vol. 0, no. 0, pp. 0–0, 2024, doi: <a href=\"https://doi.org/10.3934/jcd.2024017\">10.3934/jcd.2024017</a>.","apa":"Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., Almagro, R. T. S. M. de, &#38; Szemenyei, F. O. (2024). A new Lagrangian approach to control affine systems with a quadratic Lagrange term. <i>Journal of Computational Dynamics</i>, <i>0</i>(0), 0–0. <a href=\"https://doi.org/10.3934/jcd.2024017\">https://doi.org/10.3934/jcd.2024017</a>","short":"S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T.S.M. de Almagro, F.O. Szemenyei, Journal of Computational Dynamics 0 (2024) 0–0.","chicago":"Leyendecker, Sigrid, Sofya Maslovskaya, Sina Ober-Blöbaum, Rodrigo T. Sato Martín de Almagro, and Flóra Orsolya Szemenyei. “A New Lagrangian Approach to Control Affine Systems with a Quadratic Lagrange Term.” <i>Journal of Computational Dynamics</i> 0, no. 0 (2024): 0–0. <a href=\"https://doi.org/10.3934/jcd.2024017\">https://doi.org/10.3934/jcd.2024017</a>.","mla":"Leyendecker, Sigrid, et al. “A New Lagrangian Approach to Control Affine Systems with a Quadratic Lagrange Term.” <i>Journal of Computational Dynamics</i>, vol. 0, no. 0, American Institute of Mathematical Sciences (AIMS), 2024, pp. 0–0, doi:<a href=\"https://doi.org/10.3934/jcd.2024017\">10.3934/jcd.2024017</a>.","bibtex":"@article{Leyendecker_Maslovskaya_Ober-Blöbaum_Almagro_Szemenyei_2024, title={A new Lagrangian approach to control affine systems with a quadratic Lagrange term}, volume={0}, DOI={<a href=\"https://doi.org/10.3934/jcd.2024017\">10.3934/jcd.2024017</a>}, number={0}, journal={Journal of Computational Dynamics}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Leyendecker, Sigrid and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Almagro, Rodrigo T. Sato Martín de and Szemenyei, Flóra Orsolya}, year={2024}, pages={0–0} }","ama":"Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Almagro RTSM de, Szemenyei FO. A new Lagrangian approach to control affine systems with a quadratic Lagrange term. <i>Journal of Computational Dynamics</i>. 2024;0(0):0-0. doi:<a href=\"https://doi.org/10.3934/jcd.2024017\">10.3934/jcd.2024017</a>"},"oa":"1","has_accepted_license":"1","status":"public","volume":"0","ddc":["510"],"user_id":"87909","_id":"53101","publisher":"American Institute of Mathematical Sciences (AIMS)","page":"0-0"},{"department":[{"_id":"100"}],"type":"journal_article","date_created":"2024-04-17T12:26:51Z","abstract":[{"text":"It is known that the notion of a transitive subgroup of a permutation group\r\n$G$ extends naturally to subsets of $G$. We consider subsets of the general\r\nlinear group $\\operatorname{GL}(n,q)$ acting transitively on flag-like\r\nstructures, which are common generalisations of $t$-dimensional subspaces of\r\n$\\mathbb{F}_q^n$ and bases of $t$-dimensional subspaces of $\\mathbb{F}_q^n$. We\r\ngive structural characterisations of transitive subsets of\r\n$\\operatorname{GL}(n,q)$ using the character theory of $\\operatorname{GL}(n,q)$\r\nand interpret such subsets as designs in the conjugacy class association\r\nscheme of $\\operatorname{GL}(n,q)$. In particular we generalise a theorem of\r\nPerin on subgroups of $\\operatorname{GL}(n,q)$ acting transitively on\r\n$t$-dimensional subspaces. We survey transitive subgroups of\r\n$\\operatorname{GL}(n,q)$, showing that there is no subgroup of\r\n$\\operatorname{GL}(n,q)$ with $1<t<n$ acting transitively on $t$-dimensional\r\nsubspaces unless it contains $\\operatorname{SL}(n,q)$ or is one of two\r\nexceptional groups. On the other hand, for all fixed $t$, we show that there\r\nexist nontrivial subsets of $\\operatorname{GL}(n,q)$ that are transitive on\r\nlinearly independent $t$-tuples of $\\mathbb{F}_q^n$, which also shows the\r\nexistence of nontrivial subsets of $\\operatorname{GL}(n,q)$ that are transitive\r\non more general flag-like structures. We establish connections with orthogonal\r\npolynomials, namely the Al-Salam-Carlitz polynomials, and generalise a result\r\nby Rudvalis and Shinoda on the distribution of the number of fixed points of\r\nthe elements in $\\operatorname{GL}(n,q)$. Many of our results can be\r\ninterpreted as $q$-analogs of corresponding results for the symmetric group.","lang":"eng"}],"citation":{"mla":"Ernst, Alena, and Kai-Uwe Schmidt. “Transitivity in Finite General Linear Groups.” <i>Mathematische Zeitschrift</i>, vol. 307, no. 45, 2024, doi:<a href=\"https://doi.org/10.1007/s00209-024-03511-x\">10.1007/s00209-024-03511-x</a>.","ama":"Ernst A, Schmidt K-U. Transitivity in finite general linear groups. <i>Mathematische Zeitschrift</i>. 2024;307(45). doi:<a href=\"https://doi.org/10.1007/s00209-024-03511-x\">10.1007/s00209-024-03511-x</a>","bibtex":"@article{Ernst_Schmidt_2024, title={Transitivity in finite general linear groups}, volume={307}, DOI={<a href=\"https://doi.org/10.1007/s00209-024-03511-x\">10.1007/s00209-024-03511-x</a>}, number={45}, journal={Mathematische Zeitschrift}, author={Ernst, Alena and Schmidt, Kai-Uwe}, year={2024} }","apa":"Ernst, A., &#38; Schmidt, K.-U. (2024). Transitivity in finite general linear groups. <i>Mathematische Zeitschrift</i>, <i>307</i>(45). <a href=\"https://doi.org/10.1007/s00209-024-03511-x\">https://doi.org/10.1007/s00209-024-03511-x</a>","ieee":"A. Ernst and K.-U. Schmidt, “Transitivity in finite general linear groups,” <i>Mathematische Zeitschrift</i>, vol. 307, no. 45, 2024, doi: <a href=\"https://doi.org/10.1007/s00209-024-03511-x\">10.1007/s00209-024-03511-x</a>.","chicago":"Ernst, Alena, and Kai-Uwe Schmidt. “Transitivity in Finite General Linear Groups.” <i>Mathematische Zeitschrift</i> 307, no. 45 (2024). <a href=\"https://doi.org/10.1007/s00209-024-03511-x\">https://doi.org/10.1007/s00209-024-03511-x</a>.","short":"A. Ernst, K.-U. Schmidt, Mathematische Zeitschrift 307 (2024)."},"issue":"45","publication":"Mathematische Zeitschrift","volume":307,"doi":"10.1007/s00209-024-03511-x","user_id":"46953","_id":"53534","language":[{"iso":"eng"}],"intvolume":"       307","date_updated":"2024-06-17T10:04:29Z","author":[{"id":"46953","full_name":"Ernst, Alena","first_name":"Alena","last_name":"Ernst"},{"first_name":"Kai-Uwe","last_name":"Schmidt","full_name":"Schmidt, Kai-Uwe"}],"year":"2024","title":"Transitivity in finite general linear groups","status":"public"},{"citation":{"apa":"Sonntag, K., &#38; Peitz, S. (2024). Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping. <i>SIAM Journal on Optimization</i>, <i>34</i>(3), 2259–2286. <a href=\"https://doi.org/10.1137/23M1588512\">https://doi.org/10.1137/23M1588512</a>","mla":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping.” <i>SIAM Journal on Optimization</i>, vol. 34, no. 3, Society for Industrial and Applied Mathematics, 2024, pp. 2259–86, doi:<a href=\"https://doi.org/10.1137/23M1588512\">10.1137/23M1588512</a>.","ieee":"K. Sonntag and S. Peitz, “Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping,” <i>SIAM Journal on Optimization</i>, vol. 34, no. 3, pp. 2259–2286, 2024, doi: <a href=\"https://doi.org/10.1137/23M1588512\">10.1137/23M1588512</a>.","ama":"Sonntag K, Peitz S. Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping. <i>SIAM Journal on Optimization</i>. 2024;34(3):2259-2286. doi:<a href=\"https://doi.org/10.1137/23M1588512\">10.1137/23M1588512</a>","short":"K. Sonntag, S. Peitz, SIAM Journal on Optimization 34 (2024) 2259–2286.","chicago":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping.” <i>SIAM Journal on Optimization</i> 34, no. 3 (2024): 2259–86. <a href=\"https://doi.org/10.1137/23M1588512\">https://doi.org/10.1137/23M1588512</a>.","bibtex":"@article{Sonntag_Peitz_2024, title={Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping}, volume={34}, DOI={<a href=\"https://doi.org/10.1137/23M1588512\">10.1137/23M1588512</a>}, number={3}, journal={SIAM Journal on Optimization}, publisher={Society for Industrial and Applied Mathematics}, author={Sonntag, Konstantin and Peitz, Sebastian}, year={2024}, pages={2259–2286} }"},"status":"public","user_id":"56399","volume":34,"page":"2259 - 2286","_id":"32447","publisher":"Society for Industrial and Applied Mathematics","abstract":[{"text":"We present a new gradient-like dynamical system related to unconstrained convex smooth multiobjective optimization which involves inertial effects and asymptotic vanishing damping. To the best of our knowledge, this system is the first inertial gradient-like system for multiobjective optimization problems including asymptotic vanishing damping, expanding the ideas previously laid out in [H. Attouch and G. Garrigos, Multiobjective Optimization: An Inertial Dynamical Approach to Pareto Optima, preprint, arXiv:1506.02823, 2015]. We prove existence of solutions to this system in finite dimensions and further prove that its bounded solutions converge weakly to weakly Pareto optimal points. In addition, we obtain a convergence rate of order \\(\\mathcal{O}(t^{-2})\\) for the function values measured with a merit function. This approach presents a good basis for the development of fast gradient methods for multiobjective optimization.","lang":"eng"}],"publication":"SIAM Journal on Optimization","issue":"3","keyword":["multiobjective optimization","Pareto optimization","Lyapunov analysis","gradient-likedynamical systems","inertial dynamics","asymptotic vanishing damping","fast convergence"],"type":"journal_article","department":[{"_id":"101"},{"_id":"655"}],"date_created":"2022-07-28T11:53:02Z","date_updated":"2024-07-02T09:27:39Z","publication_status":"published","intvolume":"        34","article_type":"original","title":"Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping","year":"2024","author":[{"id":"56399","orcid":"https://orcid.org/0000-0003-3384-3496","first_name":"Konstantin","last_name":"Sonntag","full_name":"Sonntag, Konstantin"},{"full_name":"Peitz, Sebastian","last_name":"Peitz","first_name":"Sebastian","orcid":"0000-0002-3389-793X","id":"47427"}],"publication_identifier":{"issn":["1095-7189"]},"doi":"10.1137/23M1588512","language":[{"iso":"eng"}]},{"date_updated":"2024-07-24T07:23:20Z","intvolume":"      2024","year":"2024","title":"On restricted averages of Dedekind sums","status":"public","author":[{"full_name":"Minelli, P.","first_name":"P.","last_name":"Minelli"},{"full_name":"Sourmelidis, A.","last_name":"Sourmelidis","first_name":"A."},{"first_name":"Marc","last_name":"Technau","orcid":"0000-0001-9650-2459","full_name":"Technau, Marc","id":"106108"}],"doi":"10.1093/imrn/rnad283","user_id":"106108","volume":2024,"page":"8485–8502","_id":"55276","language":[{"iso":"eng"}],"issue":"10","publication":"Int. Math. Res. Not. IMRN","citation":{"apa":"Minelli, P., Sourmelidis, A., &#38; Technau, M. (2024). On restricted averages of Dedekind sums. <i>Int. Math. Res. Not. IMRN</i>, <i>2024</i>(10), 8485–8502. <a href=\"https://doi.org/10.1093/imrn/rnad283\">https://doi.org/10.1093/imrn/rnad283</a>","ieee":"P. Minelli, A. Sourmelidis, and M. Technau, “On restricted averages of Dedekind sums,” <i>Int. Math. Res. Not. IMRN</i>, vol. 2024, no. 10, pp. 8485–8502, 2024, doi: <a href=\"https://doi.org/10.1093/imrn/rnad283\">10.1093/imrn/rnad283</a>.","chicago":"Minelli, P., A. Sourmelidis, and Marc Technau. “On Restricted Averages of Dedekind Sums.” <i>Int. Math. Res. Not. IMRN</i> 2024, no. 10 (2024): 8485–8502. <a href=\"https://doi.org/10.1093/imrn/rnad283\">https://doi.org/10.1093/imrn/rnad283</a>.","short":"P. Minelli, A. Sourmelidis, M. Technau, Int. Math. Res. Not. IMRN 2024 (2024) 8485–8502.","mla":"Minelli, P., et al. “On Restricted Averages of Dedekind Sums.” <i>Int. Math. Res. Not. 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