[{"citation":{"ama":"Sonntag K. <i>First-Order Methods and Gradient Dynamical Systems for Multiobjective Optimization</i>. Paderborn University; 2025. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-2457\">10.17619/UNIPB/1-2457</a>","ieee":"K. Sonntag, <i>First-order methods and gradient dynamical systems for multiobjective optimization</i>. Paderborn University, 2025.","chicago":"Sonntag, Konstantin. <i>First-Order Methods and Gradient Dynamical Systems for Multiobjective Optimization</i>. Paderborn University, 2025. <a href=\"https://doi.org/10.17619/UNIPB/1-2457\">https://doi.org/10.17619/UNIPB/1-2457</a>.","mla":"Sonntag, Konstantin. <i>First-Order Methods and Gradient Dynamical Systems for Multiobjective Optimization</i>. Paderborn University, 2025, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-2457\">10.17619/UNIPB/1-2457</a>.","short":"K. Sonntag, First-Order Methods and Gradient Dynamical Systems for Multiobjective Optimization, Paderborn University, 2025.","bibtex":"@book{Sonntag_2025, title={First-order methods and gradient dynamical systems for multiobjective optimization}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-2457\">10.17619/UNIPB/1-2457</a>}, publisher={Paderborn University}, author={Sonntag, Konstantin}, year={2025} }","apa":"Sonntag, K. (2025). <i>First-order methods and gradient dynamical systems for multiobjective optimization</i>. Paderborn University. <a href=\"https://doi.org/10.17619/UNIPB/1-2457\">https://doi.org/10.17619/UNIPB/1-2457</a>"},"year":"2025","has_accepted_license":"1","doi":"10.17619/UNIPB/1-2457","main_file_link":[{"url":"https://digital.ub.uni-paderborn.de/hs/download/pdf/8141881","open_access":"1"}],"title":"First-order methods and gradient dynamical systems for multiobjective optimization","supervisor":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494","last_name":"Ober-Blöbaum"}],"date_created":"2025-12-03T06:55:01Z","author":[{"first_name":"Konstantin","id":"56399","full_name":"Sonntag, Konstantin","orcid":"https://orcid.org/0000-0003-3384-3496","last_name":"Sonntag"}],"date_updated":"2025-12-03T07:04:36Z","publisher":"Paderborn University","oa":"1","status":"public","abstract":[{"lang":"eng","text":"Diese Dissertation enthält Beiträge zum Bereich der Mehrzieloptimierung mit einem Fokus auf unbeschränkten Problemen, die auf einem allgemeinen Hilbertraum definiert sind. Für Mehrzieloptimierungsprobleme mit lokal Lipschitz-stetigen Zielfunktionen definieren wir ein multikriterielles Subdifferential, das wir erstmals im Kontext allgemeiner Hilberträume analysieren. Aufbauend auf diesen theoretischen Untersuchungen präsentieren wir ein Abstiegsverfahren, bei welchem in jeder Iteration eine Abstiegsrichtung mittels einer numerischen Approximation des multikriteriellen Subdifferentials bestimmt wird. Im Kontext konvexer, stetig differenzierbarer Zielfunktionen mit Lipschitz-stetigen Gradienten, führen wir eine Familie von dynamischen Gradientensystemen mit Trägheitsterm ein, die bekannte kontinuierliche Systeme aus der skalaren Optimierung verallgemeinern. Wir stellen drei neue Systeme vor: eines mit konstanter Dämpfung, eines mit asymptotisch abnehmender Dämpfung und eines, das zusätzlich eine zeitabhängige Tikhonov-Regularisierung beinhaltet. Aufbauend auf den Untersuchungen der neuen dynamischen Gradientensysteme, entwickeln wir ein beschleunigtes Gradientenverfahren zur Mehrzieloptimierung, das auf einer Diskretisierung des multikriteriellen Gradientensystems mit asymptotisch abnehmender Dämpfung beruht. Das hergeleitete Verfahren bewahrt die günstigen Konvergenzeigenschaften des kontinuierlichen Systems und erreicht eine schnellere Konvergenz als klassische Verfahren."},{"text":"This dissertation contributes to the field of multiobjective optimization, with a focus on unconstrained problems formulated in a general Hilbert space. For multiobjective optimization problems with locally Lipschitz continuous objective functions, we define a multiobjective subdifferential, which we analyze for the first time in the context of general Hilbert spaces. Building on these theoretical investigations, we present a descent method in which, at each iteration, a descent direction is determined via a numerical approximation of the multiobjective subdifferential. In the setting of convex, continuously differentiable objective functions with Lipschitz continuous gradients, we introduce a family of inertial gradient dynamical systems that generalize well-known continuous-time systems from scalar optimization. We present three novel systems: one with constant damping, one with asymptotic vanishing damping, and one combining vanishing damping with time-dependent Tikhonov regularization. Building on the investigation of the novel gradient dynamical systems, we develop an accelerated gradient method for multiobjective optimization via discretization of the multiobjective gradient system with asymptotic vanishing damping. The proposed method retains the favorable convergence properties of the continuous system while achieving faster convergence than standard approaches, such as classical methods.","lang":"eng"}],"type":"dissertation","language":[{"iso":"eng"}],"ddc":["510"],"department":[{"_id":"101"},{"_id":"530"}],"user_id":"56399","_id":"62750"},{"date_updated":"2025-12-09T09:10:01Z","publisher":"American Physical Society (APS)","date_created":"2025-12-09T09:08:39Z","author":[{"first_name":"Denis A.","full_name":"Kopylov, Denis A.","last_name":"Kopylov"},{"full_name":"Offen, Christian","id":"85279","last_name":"Offen","orcid":"0000-0002-5940-8057","first_name":"Christian"},{"last_name":"Ares","full_name":"Ares, Laura","first_name":"Laura"},{"first_name":"Boris Edgar","last_name":"Wembe Moafo","id":"95394","full_name":"Wembe Moafo, Boris Edgar"},{"full_name":"Ober-Blöbaum, Sina","id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina"},{"last_name":"Meier","orcid":"0000-0001-8864-2072","full_name":"Meier, Torsten","id":"344","first_name":"Torsten"},{"first_name":"Polina R.","id":"60286","full_name":"Sharapova, Polina R.","last_name":"Sharapova"},{"full_name":"Sperling, Jan","id":"75127","orcid":"0000-0002-5844-3205","last_name":"Sperling","first_name":"Jan"}],"volume":7,"title":"Multiphoton, multimode state classification for nonlinear optical circuits","doi":"10.1103/sv6z-v1gk","publication_status":"published","publication_identifier":{"issn":["2643-1564"]},"issue":"3","year":"2025","citation":{"ama":"Kopylov DA, Offen C, Ares L, et al. Multiphoton, multimode state classification for nonlinear optical circuits. <i>Physical Review Research</i>. 2025;7(3). doi:<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>","ieee":"D. A. Kopylov <i>et al.</i>, “Multiphoton, multimode state classification for nonlinear optical circuits,” <i>Physical Review Research</i>, vol. 7, no. 3, Art. no. 033062, 2025, doi: <a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>.","chicago":"Kopylov, Denis A., Christian Offen, Laura Ares, Boris Edgar Wembe Moafo, Sina Ober-Blöbaum, Torsten Meier, Polina R. Sharapova, and Jan Sperling. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits.” <i>Physical Review Research</i> 7, no. 3 (2025). <a href=\"https://doi.org/10.1103/sv6z-v1gk\">https://doi.org/10.1103/sv6z-v1gk</a>.","bibtex":"@article{Kopylov_Offen_Ares_Wembe Moafo_Ober-Blöbaum_Meier_Sharapova_Sperling_2025, title={Multiphoton, multimode state classification for nonlinear optical circuits}, volume={7}, DOI={<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>}, number={3033062}, journal={Physical Review Research}, publisher={American Physical Society (APS)}, author={Kopylov, Denis A. and Offen, Christian and Ares, Laura and Wembe Moafo, Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova, Polina R. and Sperling, Jan}, year={2025} }","short":"D.A. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier, P.R. Sharapova, J. Sperling, Physical Review Research 7 (2025).","mla":"Kopylov, Denis A., et al. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits.” <i>Physical Review Research</i>, vol. 7, no. 3, 033062, American Physical Society (APS), 2025, doi:<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>.","apa":"Kopylov, D. A., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S., Meier, T., Sharapova, P. R., &#38; Sperling, J. (2025). Multiphoton, multimode state classification for nonlinear optical circuits. <i>Physical Review Research</i>, <i>7</i>(3), Article 033062. <a href=\"https://doi.org/10.1103/sv6z-v1gk\">https://doi.org/10.1103/sv6z-v1gk</a>"},"intvolume":"         7","project":[{"_id":"53","name":"TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten zu funktionellen Strukturen"},{"_id":"56","name":"TRR 142 - Project Area C"},{"name":"TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen Systemen: Eine theoretische Analyse","_id":"174"},{"_id":"266","name":"PhoQC: Photonisches Quantencomputing"}],"_id":"62980","user_id":"16199","department":[{"_id":"15"},{"_id":"569"},{"_id":"170"},{"_id":"293"},{"_id":"706"},{"_id":"636"},{"_id":"35"},{"_id":"230"},{"_id":"429"},{"_id":"623"}],"article_number":"033062","language":[{"iso":"eng"}],"type":"journal_article","publication":"Physical Review Research","abstract":[{"lang":"eng","text":"<jats:p>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 is 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.</jats:p>"}],"status":"public"},{"citation":{"ama":"Meier T, Sharapova PR, Sperling J, Ober-Blöbaum S, Wembe Moafo BE, Offen C. Multiphoton, multimode state classification for nonlinear optical circuits. Published online 2025.","chicago":"Meier, Torsten, Polina R. Sharapova, Jan Sperling, Sina Ober-Blöbaum, Boris Edgar Wembe Moafo, and Christian Offen. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits,” 2025.","ieee":"T. Meier, P. R. Sharapova, J. Sperling, S. Ober-Blöbaum, B. E. Wembe Moafo, and C. Offen, “Multiphoton, multimode state classification for nonlinear optical circuits.” 2025.","mla":"Meier, Torsten, et al. <i>Multiphoton, Multimode State Classification for Nonlinear Optical Circuits</i>. 2025.","short":"T. Meier, P.R. Sharapova, J. Sperling, S. Ober-Blöbaum, B.E. Wembe Moafo, C. Offen, (2025).","bibtex":"@article{Meier_Sharapova_Sperling_Ober-Blöbaum_Wembe Moafo_Offen_2025, title={Multiphoton, multimode state classification for nonlinear optical circuits}, author={Meier, Torsten and Sharapova, Polina R. and Sperling, Jan and Ober-Blöbaum, Sina and Wembe Moafo, Boris Edgar and Offen, Christian}, year={2025} }","apa":"Meier, T., Sharapova, P. R., Sperling, J., Ober-Blöbaum, S., Wembe Moafo, B. E., &#38; Offen, C. (2025). <i>Multiphoton, multimode state classification for nonlinear optical circuits</i>."},"year":"2025","author":[{"id":"344","full_name":"Meier, Torsten","last_name":"Meier","orcid":"0000-0001-8864-2072","first_name":"Torsten"},{"full_name":"Sharapova, Polina R.","id":"60286","last_name":"Sharapova","first_name":"Polina R."},{"first_name":"Jan","orcid":"0000-0002-5844-3205","last_name":"Sperling","id":"75127","full_name":"Sperling, Jan"},{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494","first_name":"Sina"},{"last_name":"Wembe Moafo","full_name":"Wembe Moafo, Boris Edgar","id":"95394","first_name":"Boris Edgar"},{"last_name":"Offen","orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","id":"85279","first_name":"Christian"}],"date_created":"2025-12-09T08:59:27Z","date_updated":"2025-12-09T09:10:23Z","title":"Multiphoton, multimode state classification for nonlinear optical circuits","type":"preprint","status":"public","abstract":[{"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.","lang":"eng"}],"department":[{"_id":"15"},{"_id":"170"},{"_id":"293"},{"_id":"706"},{"_id":"636"},{"_id":"230"},{"_id":"623"},{"_id":"429"},{"_id":"35"}],"user_id":"16199","_id":"62979","project":[{"_id":"53","name":"TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten zu funktionellen Strukturen"},{"name":"TRR 142 - Project Area C","_id":"56"},{"_id":"174","name":"TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen Systemen: Eine theoretische Analyse"},{"_id":"266","name":"PhoQC: Photonisches Quantencomputing"}],"language":[{"iso":"eng"}]},{"status":"public","publication":"arXiv:2512.14285","type":"preprint","language":[{"iso":"eng"}],"department":[{"_id":"542"}],"user_id":"15540","external_id":{"arxiv":["2512.14285"]},"_id":"63187","citation":{"short":"A.J.J. Kidner, E. Steffen, W. Yu, ArXiv:2512.14285 (2025).","mla":"Kidner, Arnott Jeffery Joel, et al. “Edge-Coloring 4- and 5-Regular Projective Planar Graphs with No Petersen-Minor.” <i>ArXiv:2512.14285</i>, 2025.","bibtex":"@article{Kidner_Steffen_Yu_2025, title={Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor}, journal={arXiv:2512.14285}, author={Kidner, Arnott Jeffery Joel and Steffen, Eckhard and Yu, Weiqiang}, year={2025} }","apa":"Kidner, A. J. J., Steffen, E., &#38; Yu, W. (2025). Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor. In <i>arXiv:2512.14285</i>.","chicago":"Kidner, Arnott Jeffery Joel, Eckhard Steffen, and Weiqiang Yu. “Edge-Coloring 4- and 5-Regular Projective Planar Graphs with No Petersen-Minor.” <i>ArXiv:2512.14285</i>, 2025.","ieee":"A. J. J. Kidner, E. Steffen, and W. Yu, “Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor,” <i>arXiv:2512.14285</i>. 2025.","ama":"Kidner AJJ, Steffen E, Yu W. Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor. <i>arXiv:251214285</i>. Published online 2025."},"year":"2025","title":"Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor","author":[{"last_name":"Kidner","full_name":"Kidner, Arnott Jeffery Joel","id":"111755","first_name":"Arnott Jeffery Joel"},{"last_name":"Steffen","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","id":"15548","first_name":"Eckhard"},{"first_name":"Weiqiang","full_name":"Yu, Weiqiang","id":"117508","last_name":"Yu"}],"date_created":"2025-12-17T14:40:23Z","date_updated":"2025-12-18T13:17:18Z"},{"_id":"61759","external_id":{"arxiv":["2510.04675"]},"user_id":"91965","department":[{"_id":"100"}],"language":[{"iso":"eng"}],"type":"preprint","abstract":[{"lang":"eng","text":"Intersection distribution and non-hitting index are concepts introduced recently by Li and Pott as a new way to view the behaviour of a collection of finite field polynomials. With both an algebraic interpretation via the intersection of a polynomial with a set of lines, and a geometric interpretation via a (q+1)-set possessing an internal nucleus, the concepts have proved their usefulness as a new way to view various long-standing problems, and have applications in areas such as Kakeya sets. In this paper, by exploiting connections with diverse areas including the theory of algebraic curves, cyclotomy and the enumeration of irreducible polynomials, we establish new results and resolve various Open Problems of Li and Pott. We prove geometric results which shed new light on the relationship between intersection distribution and projective equivalence of polynomials, and algebraic results which describe and characterise the degree of Sf - the index of the largest non-zero entry in the intersection distribution of f. We provide new insights into the non-hitting spectrum, and show the limitations of the non-hitting index as a tool for characterisation. Finally, the benefits provided by the connections to other areas are evidenced in two short new proofs of the cubic case. "}],"status":"public","date_updated":"2025-12-19T11:23:10Z","author":[{"full_name":"Klawuhn, Lukas-André Dominik","id":"91965","last_name":"Klawuhn","orcid":"0009-0009-7736-4885","first_name":"Lukas-André Dominik"},{"last_name":"Huczynska","full_name":"Huczynska, Sophie","first_name":"Sophie"},{"first_name":"Maura","last_name":"Paterson","full_name":"Paterson, Maura"}],"date_created":"2025-10-08T14:52:20Z","title":"The Intersection Distribution: New Results and Perspectives","year":"2025","citation":{"short":"L.-A.D. Klawuhn, S. Huczynska, M. Paterson, (2025).","bibtex":"@article{Klawuhn_Huczynska_Paterson_2025, title={The Intersection Distribution: New Results and Perspectives}, author={Klawuhn, Lukas-André Dominik and Huczynska, Sophie and Paterson, Maura}, year={2025} }","mla":"Klawuhn, Lukas-André Dominik, et al. <i>The Intersection Distribution: New Results and Perspectives</i>. 2025.","apa":"Klawuhn, L.-A. D., Huczynska, S., &#38; Paterson, M. (2025). <i>The Intersection Distribution: New Results and Perspectives</i>.","ama":"Klawuhn L-AD, Huczynska S, Paterson M. The Intersection Distribution: New Results and Perspectives. Published online 2025.","ieee":"L.-A. D. Klawuhn, S. Huczynska, and M. Paterson, “The Intersection Distribution: New Results and Perspectives.” 2025.","chicago":"Klawuhn, Lukas-André Dominik, Sophie Huczynska, and Maura Paterson. “The Intersection Distribution: New Results and Perspectives,” 2025."},"page":"36"},{"external_id":{"arxiv":["2512.16079"]},"_id":"63384","user_id":"91965","department":[{"_id":"100"}],"language":[{"iso":"eng"}],"type":"preprint","abstract":[{"text":"Two fundamental ways to represent a group are as permutations and as matrices. In this paper, we study linear representations of groups that intertwine with a permutation representation. Recently, D'Alconzo and Di Scala investigated how small the matrices in such a linear representation can be. The minimal dimension of such a representation is the \\emph{linear dimension of the group action} and this has applications in cryptography and cryptosystems.\r\n\r\nWe develop the idea of linear dimension from an algebraic point of view by using the theory of permutation modules. We give structural results about representations of minimal dimension and investigate the implications of faithfulness, transitivity and primitivity on the linear dimension. Furthermore, we compute the linear dimension of several classes of finite primitive permutation groups. We also study wreath products, allowing us to determine the linear dimension of imprimitive group actions. Finally, we give the linear dimension of almost simple finite $2$-transitive groups, some of which may be used for further applications in cryptography. Our results also open up many new questions about linear representations of group actions.","lang":"eng"}],"status":"public","date_updated":"2025-12-19T11:23:41Z","date_created":"2025-12-19T11:20:46Z","author":[{"first_name":"Alice","full_name":"Devillers, Alice","last_name":"Devillers"},{"last_name":"Giudici","full_name":"Giudici, Michael","first_name":"Michael"},{"first_name":"Daniel R.","full_name":"Hawtin, Daniel R.","last_name":"Hawtin"},{"first_name":"Lukas-André Dominik","orcid":"0009-0009-7736-4885","last_name":"Klawuhn","id":"91965","full_name":"Klawuhn, Lukas-André Dominik"},{"last_name":"Morgan","full_name":"Morgan, Luke","first_name":"Luke"}],"title":"Linear dimension of group actions","year":"2025","citation":{"apa":"Devillers, A., Giudici, M., Hawtin, D. R., Klawuhn, L.-A. D., &#38; Morgan, L. (2025). <i>Linear dimension of group actions</i>.","mla":"Devillers, Alice, et al. <i>Linear Dimension of Group Actions</i>. 2025.","short":"A. Devillers, M. Giudici, D.R. Hawtin, L.-A.D. Klawuhn, L. Morgan, (2025).","bibtex":"@article{Devillers_Giudici_Hawtin_Klawuhn_Morgan_2025, title={Linear dimension of group actions}, author={Devillers, Alice and Giudici, Michael and Hawtin, Daniel R. and Klawuhn, Lukas-André Dominik and Morgan, Luke}, year={2025} }","chicago":"Devillers, Alice, Michael Giudici, Daniel R. Hawtin, Lukas-André Dominik Klawuhn, and Luke Morgan. “Linear Dimension of Group Actions,” 2025.","ieee":"A. Devillers, M. Giudici, D. R. Hawtin, L.-A. D. Klawuhn, and L. Morgan, “Linear dimension of group actions.” 2025.","ama":"Devillers A, Giudici M, Hawtin DR, Klawuhn L-AD, Morgan L. Linear dimension of group actions. Published online 2025."}},{"language":[{"iso":"eng"}],"department":[{"_id":"636"}],"user_id":"87909","external_id":{"arxiv":["2507.06024"]},"_id":"63510","status":"public","abstract":[{"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.","lang":"eng"}],"publication":"arXiv:2507.06024","type":"preprint","title":"Second order optimality conditions in a new Lagrangian formulation for optimal control problems","date_created":"2026-01-06T18:28:18Z","author":[{"full_name":"Konopik, Michael","last_name":"Konopik","first_name":"Michael"},{"first_name":"Sigrid","full_name":"Leyendecker, Sigrid","last_name":"Leyendecker"},{"full_name":"Maslovskaya, Sofya","last_name":"Maslovskaya","first_name":"Sofya"},{"last_name":"Sina Ober-Blöbaum","full_name":"Sina Ober-Blöbaum, Sina Ober-Blöbaum","first_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","citation":{"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>.","short":"M. Konopik, S. Leyendecker, S. Maslovskaya, S.O.-B. Sina Ober-Blöbaum, R.T.S.M. de Almagro, ArXiv:2507.06024 (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.","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.","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.","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."},"year":"2025"},{"date_created":"2025-05-05T09:35:31Z","author":[{"full_name":"Konopik, Michael","last_name":"Konopik","first_name":"Michael"},{"first_name":"Rodrigo","full_name":"T. Sato Martín de Almagro, Rodrigo","last_name":"T. Sato Martín de Almagro"},{"id":"87909","full_name":"Maslovskaya, Sofya","last_name":"Maslovskaya","first_name":"Sofya"},{"full_name":"Ober-Blöbaum, Sina","id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina"},{"last_name":"Leyendecker","full_name":"Leyendecker, Sigrid","first_name":"Sigrid"}],"volume":36,"date_updated":"2026-01-06T18:26:57Z","doi":"10.1007/s00332-025-10229-5","title":"Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term","issue":"11","citation":{"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>","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>.","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>.","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>","short":"M. Konopik, R. T. Sato Martín de Almagro, S. Maslovskaya, S. Ober-Blöbaum, S. Leyendecker, Journal of Nonlinear Science 36 (2025).","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} }","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>."},"intvolume":"        36","year":"2025","user_id":"87909","department":[{"_id":"636"}],"_id":"59797","language":[{"iso":"eng"}],"type":"journal_article","publication":"Journal of Nonlinear Science","status":"public"},{"_id":"59799","user_id":"87909","department":[{"_id":"636"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Nonlinearity","status":"public","date_updated":"2026-01-06T18:24:40Z","author":[{"full_name":"Konopik, Michael","last_name":"Konopik","first_name":"Michael"},{"full_name":"Leyendecker, Sigrid","last_name":"Leyendecker","first_name":"Sigrid"},{"last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya","id":"87909","first_name":"Sofya"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Rodrigo","full_name":"T. Sato Martín de Almagro, Rodrigo","last_name":"T. Sato Martín de Almagro"}],"date_created":"2025-05-05T09:37:50Z","volume":38,"title":"A new Lagrangian approach to optimal control of second-order systems","doi":"10.1088/1361-6544/ae1d08","issue":"11","year":"2025","citation":{"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>.","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>.","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>","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>","short":"M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R. T. Sato Martín de Almagro, Nonlinearity 38 (2025).","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>."},"intvolume":"        38"},{"publisher":"Springer Science and Business Media LLC","date_updated":"2024-02-08T08:05:54Z","date_created":"2024-02-07T07:23:23Z","author":[{"last_name":"Gebken","id":"32643","full_name":"Gebken, Bennet","first_name":"Bennet"}],"title":"A note on the convergence of deterministic gradient sampling in nonsmooth optimization","doi":"10.1007/s10589-024-00552-0","publication_identifier":{"issn":["0926-6003","1573-2894"]},"publication_status":"published","year":"2024","citation":{"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>","short":"B. Gebken, Computational Optimization and Applications (2024).","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} }","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>.","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>","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>.","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>."},"_id":"51208","department":[{"_id":"101"}],"user_id":"32643","keyword":["Applied Mathematics","Computational Mathematics","Control and Optimization"],"language":[{"iso":"eng"}],"publication":"Computational Optimization and Applications","type":"journal_article","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"}],"status":"public"},{"status":"public","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"}],"type":"journal_article","publication":"Journal of Optimization Theory and Applications","language":[{"iso":"eng"}],"user_id":"56399","department":[{"_id":"101"},{"_id":"655"}],"_id":"46019","citation":{"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>","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>.","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>.","short":"K. Sonntag, S. Peitz, Journal of Optimization Theory and Applications (2024).","bibtex":"@article{Sonntag_Peitz_2024, title={Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems}, DOI={<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>"},"year":"2024","publication_status":"published","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10957-024-02389-3.pdf","open_access":"1"}],"doi":"10.1007/s10957-024-02389-3","title":"Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems","date_created":"2023-07-12T06:35:58Z","author":[{"last_name":"Sonntag","orcid":"https://orcid.org/0000-0003-3384-3496","full_name":"Sonntag, Konstantin","id":"56399","first_name":"Konstantin"},{"first_name":"Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427","full_name":"Peitz, Sebastian"}],"oa":"1","publisher":"Springer","date_updated":"2024-02-21T10:13:33Z"},{"date_created":"2024-02-13T09:35:26Z","author":[{"id":"56399","full_name":"Sonntag, Konstantin","last_name":"Sonntag","orcid":"https://orcid.org/0000-0003-3384-3496","first_name":"Konstantin"},{"id":"32643","full_name":"Gebken, Bennet","last_name":"Gebken","first_name":"Bennet"},{"last_name":"Müller","full_name":"Müller, Georg","first_name":"Georg"},{"orcid":"0000-0002-3389-793X","last_name":"Peitz","full_name":"Peitz, Sebastian","id":"47427","first_name":"Sebastian"},{"last_name":"Volkwein","full_name":"Volkwein, Stefan","first_name":"Stefan"}],"oa":"1","date_updated":"2024-02-21T10:21:03Z","main_file_link":[{"url":"https://arxiv.org/abs/2402.06376","open_access":"1"}],"title":"A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces","has_accepted_license":"1","citation":{"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).","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.","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.","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."},"year":"2024","department":[{"_id":"101"},{"_id":"655"}],"user_id":"56399","external_id":{"arxiv":["\t2402.06376"]},"_id":"51334","language":[{"iso":"eng"}],"publication":"arXiv:2402.06376","type":"preprint","status":"public","abstract":[{"text":"The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points, where in each iteration, an approximation of the subdifferential is computed in an efficient manner and then used to compute a common descent direction for all objective functions. To prove convergence, we present some new optimality results for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these, we can show that every accumulation point of the sequence generated by our algorithm is Pareto critical under common assumptions. Computational efficiency for finding Pareto critical points is numerically demonstrated for multiobjective optimal control of an obstacle problem.","lang":"eng"}]},{"year":"2024","issue":"2","title":"Heteroclinic dynamics in network dynamical systems with higher-order interactions","publisher":"Oxford University Press (OUP)","date_created":"2024-03-22T09:04:57Z","abstract":[{"lang":"eng","text":"Heteroclinic structures organize global features of dynamical systems. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analysed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures."}],"file":[{"content_type":"application/pdf","relation":"main_file","success":1,"creator":"svdg","date_created":"2024-03-22T09:06:07Z","date_updated":"2024-03-22T09:06:07Z","access_level":"closed","file_name":"heteroclinic-dynamics-in-network-dynamical-systems-with-higher-order-interactions.pdf","file_id":"52728","file_size":649155}],"publication":"Journal of Complex Networks","ddc":["510"],"keyword":["Applied Mathematics","Computational Mathematics","Control and Optimization","Management Science and Operations Research","Computer Networks and Communications"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["2309.02006"]},"citation":{"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>.","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>","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>","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>.","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} }","short":"C. Bick, S. von der Gracht, Journal of Complex Networks 12 (2024)."},"intvolume":"        12","publication_status":"published","has_accepted_license":"1","publication_identifier":{"issn":["2051-1329"]},"main_file_link":[{"url":"https://academic.oup.com/comnet/article-pdf/12/2/cnae009/56832119/cnae009.pdf","open_access":"1"}],"doi":"10.1093/comnet/cnae009","date_updated":"2024-03-22T09:11:53Z","oa":"1","author":[{"last_name":"Bick","full_name":"Bick, Christian","first_name":"Christian"},{"last_name":"von der Gracht","orcid":"0000-0002-8054-2058","id":"97359","full_name":"von der Gracht, Sören","first_name":"Sören"}],"volume":12,"status":"public","type":"journal_article","article_type":"original","file_date_updated":"2024-03-22T09:06:07Z","_id":"52726","user_id":"97359","department":[{"_id":"101"}]},{"doi":"10.1007/s00493-023-00078-9","title":"Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs","date_created":"2023-12-20T10:31:27Z","author":[{"first_name":"Yulai","full_name":"Ma, Yulai","id":"92748","last_name":"Ma"},{"first_name":"Davide","full_name":"Mattiolo, Davide","last_name":"Mattiolo"},{"first_name":"Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401","id":"15548","full_name":"Steffen, Eckhard"},{"id":"88145","full_name":"Wolf, Isaak Hieronymus","last_name":"Wolf","first_name":"Isaak Hieronymus"}],"volume":44,"date_updated":"2024-03-22T12:11:35Z","publisher":"Springer Science and Business Media LLC","citation":{"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>.","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>.","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} }","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>.","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>"},"page":"429-440","intvolume":"        44","year":"2024","publication_status":"published","publication_identifier":{"issn":["0209-9683","1439-6912"]},"language":[{"iso":"eng"}],"keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics"],"user_id":"15540","department":[{"_id":"542"}],"_id":"49905","status":"public","abstract":[{"lang":"eng","text":"For 0 ≤ t ≤ r let m(t, r) be the maximum number s such that every t-edge-connected r-graph has s pairwise disjoint perfect matchings. There are only a few values of m(t, r) known, for instance m(3, 3) = m(4, r) = 1, and m(t, r) ≤ r − 2 for all t \u0003 = 5,\r\nand m(t, r) ≤ r − 3 if r is even. We prove that m(2l, r) ≤ 3l − 6 for every l ≥ 3 and r ≥ 2l."}],"type":"journal_article","publication":"Combinatorica"},{"ddc":["510"],"keyword":["Optimal control problem","Lagrangian system","Hamiltonian system","Variations","Pontryagin's maximum principle."],"language":[{"iso":"eng"}],"abstract":[{"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.","lang":"eng"}],"publication":"Journal of Computational Dynamics","title":"A new Lagrangian approach to control affine systems with a quadratic Lagrange term","publisher":"American Institute of Mathematical Sciences (AIMS)","date_created":"2024-03-28T15:58:02Z","year":"2024","issue":"0","article_type":"original","_id":"53101","user_id":"87909","department":[{"_id":"636"}],"status":"public","type":"journal_article","main_file_link":[{"url":"https://www.aimsciences.org/article/doi/10.3934/jcd.2024017","open_access":"1"}],"doi":"10.3934/jcd.2024017","date_updated":"2024-03-28T16:07:34Z","oa":"1","author":[{"first_name":"Sigrid","full_name":"Leyendecker, Sigrid","last_name":"Leyendecker"},{"first_name":"Sofya","id":"87909","full_name":"Maslovskaya, Sofya","last_name":"Maslovskaya"},{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494","first_name":"Sina"},{"first_name":"Rodrigo T. Sato Martín de","last_name":"Almagro","full_name":"Almagro, Rodrigo T. Sato Martín de"},{"last_name":"Szemenyei","full_name":"Szemenyei, Flóra Orsolya","first_name":"Flóra Orsolya"}],"volume":"0","citation":{"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} }","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.","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>.","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>","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>.","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>.","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>"},"page":"0-0","publication_status":"published","has_accepted_license":"1","publication_identifier":{"issn":["2158-2491","2158-2505"]}},{"publication":"Mathematische Zeitschrift","type":"journal_article","status":"public","abstract":[{"lang":"eng","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."}],"department":[{"_id":"100"}],"user_id":"46953","_id":"53534","language":[{"iso":"eng"}],"issue":"45","intvolume":"       307","citation":{"short":"A. Ernst, K.-U. Schmidt, Mathematische Zeitschrift 307 (2024).","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>.","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>.","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>"},"year":"2024","volume":307,"author":[{"first_name":"Alena","id":"46953","full_name":"Ernst, Alena","last_name":"Ernst"},{"last_name":"Schmidt","full_name":"Schmidt, Kai-Uwe","first_name":"Kai-Uwe"}],"date_created":"2024-04-17T12:26:51Z","date_updated":"2024-06-17T10:04:29Z","doi":"10.1007/s00209-024-03511-x","title":"Transitivity in finite general linear groups"},{"publisher":"Society for Industrial and Applied Mathematics","date_updated":"2024-07-02T09:27:39Z","volume":34,"date_created":"2022-07-28T11:53:02Z","author":[{"first_name":"Konstantin","last_name":"Sonntag","orcid":"https://orcid.org/0000-0003-3384-3496","id":"56399","full_name":"Sonntag, Konstantin"},{"full_name":"Peitz, Sebastian","id":"47427","orcid":"0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian"}],"title":"Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping","doi":"10.1137/23M1588512","publication_identifier":{"issn":["1095-7189"]},"publication_status":"published","issue":"3","year":"2024","intvolume":"        34","page":"2259 - 2286","citation":{"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>.","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>.","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>","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>","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>.","short":"K. Sonntag, S. Peitz, SIAM Journal on Optimization 34 (2024) 2259–2286.","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} }"},"_id":"32447","department":[{"_id":"101"},{"_id":"655"}],"user_id":"56399","keyword":["multiobjective optimization","Pareto optimization","Lyapunov analysis","gradient-likedynamical systems","inertial dynamics","asymptotic vanishing damping","fast convergence"],"article_type":"original","language":[{"iso":"eng"}],"publication":"SIAM Journal on Optimization","type":"journal_article","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"}],"status":"public"},{"publication":"Int. Math. Res. Not. IMRN","type":"journal_article","status":"public","_id":"55276","department":[{"_id":"102"}],"user_id":"106108","language":[{"iso":"eng"}],"issue":"10","year":"2024","intvolume":"      2024","page":"8485–8502","citation":{"ama":"Minelli P, Sourmelidis A, Technau M. On restricted averages of Dedekind sums. <i>Int Math Res Not IMRN</i>. 2024;2024(10):8485–8502. 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>.","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>.","bibtex":"@article{Minelli_Sourmelidis_Technau_2024, title={On restricted averages of Dedekind sums}, volume={2024}, DOI={<a href=\"https://doi.org/10.1093/imrn/rnad283\">10.1093/imrn/rnad283</a>}, number={10}, journal={Int. Math. Res. Not. IMRN}, author={Minelli, P. and Sourmelidis, A. and Technau, Marc}, year={2024}, pages={8485–8502} }","mla":"Minelli, P., et al. “On Restricted Averages of Dedekind Sums.” <i>Int. Math. Res. Not. IMRN</i>, vol. 2024, no. 10, 2024, pp. 8485–8502, doi:<a href=\"https://doi.org/10.1093/imrn/rnad283\">10.1093/imrn/rnad283</a>.","short":"P. Minelli, A. Sourmelidis, M. Technau, Int. Math. Res. Not. IMRN 2024 (2024) 8485–8502.","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>"},"date_updated":"2024-07-24T07:23:20Z","volume":2024,"author":[{"last_name":"Minelli","full_name":"Minelli, P.","first_name":"P."},{"last_name":"Sourmelidis","full_name":"Sourmelidis, A.","first_name":"A."},{"id":"106108","full_name":"Technau, Marc","last_name":"Technau","orcid":"0000-0001-9650-2459","first_name":"Marc"}],"date_created":"2024-07-16T11:09:00Z","title":"On restricted averages of Dedekind sums","doi":"10.1093/imrn/rnad283"},{"user_id":"106108","department":[{"_id":"102"}],"_id":"55278","language":[{"iso":"eng"}],"extern":"1","type":"journal_article","publication":"Proc. Amer. Math. Soc.","status":"public","date_created":"2024-07-16T11:09:01Z","author":[{"first_name":"Marc","id":"106108","full_name":"Technau, Marc","last_name":"Technau","orcid":"0000-0001-9650-2459"}],"volume":152,"date_updated":"2024-07-24T07:26:12Z","doi":"10.1090/proc/16520","title":"Remark on the Farey fraction spin chain","issue":"1","citation":{"ama":"Technau M. Remark on the Farey fraction spin chain. <i>Proc Amer Math Soc</i>. 2024;152(1):63–69. doi:<a href=\"https://doi.org/10.1090/proc/16520\">10.1090/proc/16520</a>","ieee":"M. Technau, “Remark on the Farey fraction spin chain,” <i>Proc. Amer. Math. Soc.</i>, vol. 152, no. 1, pp. 63–69, 2024, doi: <a href=\"https://doi.org/10.1090/proc/16520\">10.1090/proc/16520</a>.","chicago":"Technau, Marc. “Remark on the Farey Fraction Spin Chain.” <i>Proc. Amer. Math. Soc.</i> 152, no. 1 (2024): 63–69. <a href=\"https://doi.org/10.1090/proc/16520\">https://doi.org/10.1090/proc/16520</a>.","mla":"Technau, Marc. “Remark on the Farey Fraction Spin Chain.” <i>Proc. Amer. Math. Soc.</i>, vol. 152, no. 1, 2024, pp. 63–69, doi:<a href=\"https://doi.org/10.1090/proc/16520\">10.1090/proc/16520</a>.","bibtex":"@article{Technau_2024, title={Remark on the Farey fraction spin chain}, volume={152}, DOI={<a href=\"https://doi.org/10.1090/proc/16520\">10.1090/proc/16520</a>}, number={1}, journal={Proc. Amer. Math. Soc.}, author={Technau, Marc}, year={2024}, pages={63–69} }","short":"M. Technau, Proc. Amer. Math. Soc. 152 (2024) 63–69.","apa":"Technau, M. (2024). Remark on the Farey fraction spin chain. <i>Proc. Amer. Math. Soc.</i>, <i>152</i>(1), 63–69. <a href=\"https://doi.org/10.1090/proc/16520\">https://doi.org/10.1090/proc/16520</a>"},"intvolume":"       152","page":"63–69","year":"2024"},{"quality_controlled":"1","issue":"1","year":"2024","publisher":"AIP Publishing","date_created":"2023-08-10T08:24:48Z","title":"Learning of discrete models of variational PDEs from data","publication":"Chaos","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. "}],"file":[{"creator":"coffen","date_created":"2024-01-09T10:48:38Z","date_updated":"2024-01-09T10:48:38Z","access_level":"open_access","file_id":"50376","file_name":"Accepted manuscript with AIP banner CHA23-AR-01370.pdf","title":"Accepted Manuscript Chaos","file_size":13222105,"content_type":"application/pdf","relation":"main_file"},{"relation":"main_file","content_type":"application/pdf","title":"Learning of discrete models of variational PDEs from data","description":"We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train\na neural network model of a discrete Lagrangian density such that the discrete Euler–Lagrange equations are consistent\nwith the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian\ndensities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for\nthe training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers\nguarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical\nsimulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory\nsuch as travelling waves. This is possible even when travelling waves are not present in the training data. This is\ncompared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces\ncontaining structurally simple solutions when these are not present in the training data. Ideas are demonstrated on\nexamples based on the wave equation and the Schrödinger equation.","file_size":12960884,"file_name":"LDensityPDE_AIP.pdf","file_id":"50390","access_level":"open_access","date_updated":"2024-01-09T11:19:49Z","creator":"coffen","date_created":"2024-01-09T11:19:49Z"}],"external_id":{"arxiv":["2308.05082 "]},"ddc":["510"],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1054-1500"]},"has_accepted_license":"1","publication_status":"published","related_material":{"link":[{"url":"https://github.com/Christian-Offen/DLNN_pde","description":"GitHub","relation":"software"}]},"intvolume":"        34","citation":{"bibtex":"@article{Offen_Ober-Blöbaum_2024, title={Learning of discrete models of variational PDEs from data}, volume={34}, DOI={<a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>}, number={1013104}, journal={Chaos}, publisher={AIP Publishing}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2024} }","short":"C. Offen, S. Ober-Blöbaum, Chaos 34 (2024).","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational PDEs from Data.” <i>Chaos</i>, vol. 34, no. 1, 013104, AIP Publishing, 2024, doi:<a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>.","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2024). Learning of discrete models of variational PDEs from data. <i>Chaos</i>, <i>34</i>(1), Article 013104. <a href=\"https://doi.org/10.1063/5.0172287\">https://doi.org/10.1063/5.0172287</a>","ieee":"C. Offen and S. Ober-Blöbaum, “Learning of discrete models of variational PDEs from data,” <i>Chaos</i>, vol. 34, no. 1, Art. no. 013104, 2024, doi: <a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>.","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational PDEs from Data.” <i>Chaos</i> 34, no. 1 (2024). <a href=\"https://doi.org/10.1063/5.0172287\">https://doi.org/10.1063/5.0172287</a>.","ama":"Offen C, Ober-Blöbaum S. Learning of discrete models of variational PDEs from data. <i>Chaos</i>. 2024;34(1). doi:<a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>"},"oa":"1","date_updated":"2024-08-12T13:45:43Z","volume":34,"author":[{"first_name":"Christian","full_name":"Offen, Christian","id":"85279","orcid":"0000-0002-5940-8057","last_name":"Offen"},{"full_name":"Ober-Blöbaum, Sina","id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina"}],"doi":"10.1063/5.0172287","type":"journal_article","status":"public","_id":"46469","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"department":[{"_id":"636"}],"user_id":"85279","article_number":"013104","article_type":"original","file_date_updated":"2024-01-09T11:19:49Z"}]