---
_id: '62750'
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.'
- lang: eng
  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.'
author:
- first_name: Konstantin
  full_name: Sonntag, Konstantin
  id: '56399'
  last_name: Sonntag
  orcid: https://orcid.org/0000-0003-3384-3496
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>
  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>
  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} }'
  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>.
  ieee: K. Sonntag, <i>First-order methods and gradient dynamical systems for multiobjective
    optimization</i>. Paderborn University, 2025.
  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.
date_created: 2025-12-03T06:55:01Z
date_updated: 2025-12-03T07:04:36Z
ddc:
- '510'
department:
- _id: '101'
- _id: '530'
doi: 10.17619/UNIPB/1-2457
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://digital.ub.uni-paderborn.de/hs/download/pdf/8141881
oa: '1'
publisher: Paderborn University
status: public
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
title: First-order methods and gradient dynamical systems for multiobjective optimization
type: dissertation
user_id: '56399'
year: '2025'
...
---
_id: '62980'
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>
article_number: '033062'
author:
- first_name: Denis A.
  full_name: Kopylov, Denis A.
  last_name: Kopylov
- first_name: Christian
  full_name: Offen, Christian
  id: '85279'
  last_name: Offen
  orcid: 0000-0002-5940-8057
- first_name: Laura
  full_name: Ares, Laura
  last_name: Ares
- first_name: Boris Edgar
  full_name: Wembe Moafo, Boris Edgar
  id: '95394'
  last_name: Wembe Moafo
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  id: '16494'
  last_name: Ober-Blöbaum
- first_name: Torsten
  full_name: Meier, Torsten
  id: '344'
  last_name: Meier
  orcid: 0000-0001-8864-2072
- first_name: Polina R.
  full_name: Sharapova, Polina R.
  id: '60286'
  last_name: Sharapova
- first_name: Jan
  full_name: Sperling, Jan
  id: '75127'
  last_name: Sperling
  orcid: 0000-0002-5844-3205
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>
  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>
  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} }'
  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>.
  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>.'
  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>.
  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).
date_created: 2025-12-09T09:08:39Z
date_updated: 2025-12-09T09:10:01Z
department:
- _id: '15'
- _id: '569'
- _id: '170'
- _id: '293'
- _id: '706'
- _id: '636'
- _id: '35'
- _id: '230'
- _id: '429'
- _id: '623'
doi: 10.1103/sv6z-v1gk
intvolume: '         7'
issue: '3'
language:
- iso: eng
project:
- _id: '53'
  name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
    zu funktionellen Strukturen'
- _id: '56'
  name: TRR 142 - Project Area C
- _id: '174'
  name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
    Systemen: Eine theoretische Analyse'
- _id: '266'
  name: 'PhoQC: Photonisches Quantencomputing'
publication: Physical Review Research
publication_identifier:
  issn:
  - 2643-1564
publication_status: published
publisher: American Physical Society (APS)
status: public
title: Multiphoton, multimode state classification for nonlinear optical circuits
type: journal_article
user_id: '16199'
volume: 7
year: '2025'
...
---
_id: '62979'
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.
author:
- first_name: Torsten
  full_name: Meier, Torsten
  id: '344'
  last_name: Meier
  orcid: 0000-0001-8864-2072
- first_name: Polina R.
  full_name: Sharapova, Polina R.
  id: '60286'
  last_name: Sharapova
- first_name: Jan
  full_name: Sperling, Jan
  id: '75127'
  last_name: Sperling
  orcid: 0000-0002-5844-3205
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  id: '16494'
  last_name: Ober-Blöbaum
- first_name: Boris Edgar
  full_name: Wembe Moafo, Boris Edgar
  id: '95394'
  last_name: Wembe Moafo
- first_name: Christian
  full_name: Offen, Christian
  id: '85279'
  last_name: Offen
  orcid: 0000-0002-5940-8057
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.
  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>.
  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} }'
  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).
date_created: 2025-12-09T08:59:27Z
date_updated: 2025-12-09T09:10:23Z
department:
- _id: '15'
- _id: '170'
- _id: '293'
- _id: '706'
- _id: '636'
- _id: '230'
- _id: '623'
- _id: '429'
- _id: '35'
language:
- iso: eng
project:
- _id: '53'
  name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
    zu funktionellen Strukturen'
- _id: '56'
  name: TRR 142 - Project Area C
- _id: '174'
  name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
    Systemen: Eine theoretische Analyse'
- _id: '266'
  name: 'PhoQC: Photonisches Quantencomputing'
status: public
title: Multiphoton, multimode state classification for nonlinear optical circuits
type: preprint
user_id: '16199'
year: '2025'
...
---
_id: '63187'
author:
- first_name: Arnott Jeffery Joel
  full_name: Kidner, Arnott Jeffery Joel
  id: '111755'
  last_name: Kidner
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Weiqiang
  full_name: Yu, Weiqiang
  id: '117508'
  last_name: Yu
citation:
  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.
  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>.
  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}
    }'
  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.
  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.
  short: A.J.J. Kidner, E. Steffen, W. Yu, ArXiv:2512.14285 (2025).
date_created: 2025-12-17T14:40:23Z
date_updated: 2025-12-18T13:17:18Z
department:
- _id: '542'
external_id:
  arxiv:
  - '2512.14285'
language:
- iso: eng
publication: arXiv:2512.14285
status: public
title: Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor
type: preprint
user_id: '15540'
year: '2025'
...
---
_id: '61759'
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. '
author:
- first_name: Lukas-André Dominik
  full_name: Klawuhn, Lukas-André Dominik
  id: '91965'
  last_name: Klawuhn
  orcid: 0009-0009-7736-4885
- first_name: Sophie
  full_name: Huczynska, Sophie
  last_name: Huczynska
- first_name: Maura
  full_name: Paterson, Maura
  last_name: Paterson
citation:
  ama: 'Klawuhn L-AD, Huczynska S, Paterson M. The Intersection Distribution: New
    Results and Perspectives. Published online 2025.'
  apa: 'Klawuhn, L.-A. D., Huczynska, S., &#38; Paterson, M. (2025). <i>The Intersection
    Distribution: New Results and Perspectives</i>.'
  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} }'
  chicago: 'Klawuhn, Lukas-André Dominik, Sophie Huczynska, and Maura Paterson. “The
    Intersection Distribution: New Results and Perspectives,” 2025.'
  ieee: 'L.-A. D. Klawuhn, S. Huczynska, and M. Paterson, “The Intersection Distribution:
    New Results and Perspectives.” 2025.'
  mla: 'Klawuhn, Lukas-André Dominik, et al. <i>The Intersection Distribution: New
    Results and Perspectives</i>. 2025.'
  short: L.-A.D. Klawuhn, S. Huczynska, M. Paterson, (2025).
date_created: 2025-10-08T14:52:20Z
date_updated: 2025-12-19T11:23:10Z
department:
- _id: '100'
external_id:
  arxiv:
  - '2510.04675'
language:
- iso: eng
page: '36'
status: public
title: 'The Intersection Distribution: New Results and Perspectives'
type: preprint
user_id: '91965'
year: '2025'
...
---
_id: '63384'
abstract:
- lang: eng
  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."
author:
- first_name: Alice
  full_name: Devillers, Alice
  last_name: Devillers
- first_name: Michael
  full_name: Giudici, Michael
  last_name: Giudici
- first_name: Daniel R.
  full_name: Hawtin, Daniel R.
  last_name: Hawtin
- first_name: Lukas-André Dominik
  full_name: Klawuhn, Lukas-André Dominik
  id: '91965'
  last_name: Klawuhn
  orcid: 0009-0009-7736-4885
- first_name: Luke
  full_name: Morgan, Luke
  last_name: Morgan
citation:
  ama: Devillers A, Giudici M, Hawtin DR, Klawuhn L-AD, Morgan L. Linear dimension
    of group actions. Published online 2025.
  apa: Devillers, A., Giudici, M., Hawtin, D. R., Klawuhn, L.-A. D., &#38; Morgan,
    L. (2025). <i>Linear dimension of group actions</i>.
  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.
  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).
date_created: 2025-12-19T11:20:46Z
date_updated: 2025-12-19T11:23:41Z
department:
- _id: '100'
external_id:
  arxiv:
  - '2512.16079'
language:
- iso: eng
status: public
title: Linear dimension of group actions
type: preprint
user_id: '91965'
year: '2025'
...
---
_id: '63510'
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.
author:
- first_name: Michael
  full_name: Konopik, Michael
  last_name: Konopik
- first_name: Sigrid
  full_name: Leyendecker, Sigrid
  last_name: Leyendecker
- first_name: Sofya
  full_name: Maslovskaya, Sofya
  last_name: Maslovskaya
- first_name: Sina Ober-Blöbaum
  full_name: Sina Ober-Blöbaum, Sina Ober-Blöbaum
  last_name: Sina Ober-Blöbaum
- first_name: Rodrigo T. Sato Martín de
  full_name: Almagro, Rodrigo T. Sato Martín de
  last_name: Almagro
citation:
  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.
  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>.
  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} }'
  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.
  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.
  mla: Konopik, Michael, et al. “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).
date_created: 2026-01-06T18:28:18Z
date_updated: 2026-01-06T18:29:15Z
department:
- _id: '636'
external_id:
  arxiv:
  - '2507.06024'
language:
- iso: eng
publication: arXiv:2507.06024
status: public
title: Second order optimality conditions in a new Lagrangian formulation for optimal
  control problems
type: preprint
user_id: '87909'
year: '2025'
...
---
_id: '59797'
author:
- first_name: Michael
  full_name: Konopik, Michael
  last_name: Konopik
- first_name: Rodrigo
  full_name: T. Sato Martín de Almagro, Rodrigo
  last_name: T. Sato Martín de Almagro
- first_name: Sofya
  full_name: Maslovskaya, Sofya
  id: '87909'
  last_name: Maslovskaya
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  id: '16494'
  last_name: Ober-Blöbaum
- first_name: Sigrid
  full_name: Leyendecker, Sigrid
  last_name: Leyendecker
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>
  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>
  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} }'
  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>.
  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>.'
  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>.
  short: M. Konopik, R. T. Sato Martín de Almagro, S. Maslovskaya, S. Ober-Blöbaum,
    S. Leyendecker, Journal of Nonlinear Science 36 (2025).
date_created: 2025-05-05T09:35:31Z
date_updated: 2026-01-06T18:26:57Z
department:
- _id: '636'
doi: 10.1007/s00332-025-10229-5
intvolume: '        36'
issue: '11'
language:
- iso: eng
publication: Journal of Nonlinear Science
status: public
title: Variational integrators for a new Lagrangian approach to control affine systems
  with a quadratic Lagrange term
type: journal_article
user_id: '87909'
volume: 36
year: '2025'
...
---
_id: '59799'
author:
- first_name: Michael
  full_name: Konopik, Michael
  last_name: Konopik
- first_name: Sigrid
  full_name: Leyendecker, Sigrid
  last_name: Leyendecker
- first_name: Sofya
  full_name: Maslovskaya, Sofya
  id: '87909'
  last_name: Maslovskaya
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  id: '16494'
  last_name: Ober-Blöbaum
- first_name: Rodrigo
  full_name: T. Sato Martín de Almagro, Rodrigo
  last_name: T. Sato Martín de Almagro
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>
  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>
  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} }'
  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>.'
  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>.
  short: M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R. T. Sato Martín
    de Almagro, Nonlinearity 38 (2025).
date_created: 2025-05-05T09:37:50Z
date_updated: 2026-01-06T18:24:40Z
department:
- _id: '636'
doi: 10.1088/1361-6544/ae1d08
intvolume: '        38'
issue: '11'
language:
- iso: eng
publication: Nonlinearity
status: public
title: A new Lagrangian approach to optimal control of second-order systems
type: journal_article
user_id: '87909'
volume: 38
year: '2025'
...
---
_id: '51208'
abstract:
- lang: eng
  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>
author:
- first_name: Bennet
  full_name: Gebken, Bennet
  id: '32643'
  last_name: Gebken
citation:
  ama: Gebken B. A note on the convergence of deterministic gradient sampling in nonsmooth
    optimization. <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>
  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>
  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} }'
  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>.'
  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).
date_created: 2024-02-07T07:23:23Z
date_updated: 2024-02-08T08:05:54Z
department:
- _id: '101'
doi: 10.1007/s10589-024-00552-0
keyword:
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
language:
- iso: eng
publication: Computational Optimization and Applications
publication_identifier:
  issn:
  - 0926-6003
  - 1573-2894
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: A note on the convergence of deterministic gradient sampling in nonsmooth optimization
type: journal_article
user_id: '32643'
year: '2024'
...
---
_id: '46019'
abstract:
- lang: eng
  text: We derive efficient algorithms to compute weakly Pareto optimal solutions
    for smooth, convex and unconstrained multiobjective optimization problems in general
    Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical
    system in the multiobjective setting, which trajectories converge weakly to Pareto
    optimal solutions. Discretization of this system yields an inertial multiobjective
    algorithm which generates sequences that converge weakly to Pareto optimal solutions.
    We employ Nesterov acceleration to define an algorithm with an improved convergence
    rate compared to the plain multiobjective steepest descent method (Algorithm 1).
    A further improvement in terms of efficiency is achieved by avoiding the solution
    of a quadratic subproblem to compute a common step direction for all objective
    functions, which is usually required in first-order methods. Using a different
    discretization of our inertial gradient-like dynamical system, we obtain an accelerated
    multiobjective gradient method that does not require the solution of a subproblem
    in each step (Algorithm 2). While this algorithm does not converge in general,
    it yields good results on test problems while being faster than standard steepest
    descent.
author:
- first_name: Konstantin
  full_name: Sonntag, Konstantin
  id: '56399'
  last_name: Sonntag
  orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: 0000-0002-3389-793X
citation:
  ama: Sonntag K, Peitz S. Fast Multiobjective Gradient Methods with Nesterov Acceleration
    via Inertial Gradient-Like Systems. <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>
  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>
  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} }'
  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>.
  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>.'
  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).
date_created: 2023-07-12T06:35:58Z
date_updated: 2024-02-21T10:13:33Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/s10957-024-02389-3
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://link.springer.com/content/pdf/10.1007/s10957-024-02389-3.pdf
oa: '1'
publication: Journal of Optimization Theory and Applications
publication_status: published
publisher: Springer
status: public
title: Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial
  Gradient-Like Systems
type: journal_article
user_id: '56399'
year: '2024'
...
---
_id: '51334'
abstract:
- lang: eng
  text: The efficient optimization method for locally Lipschitz continuous multiobjective
    optimization problems from [1] is extended from finite-dimensional problems to
    general Hilbert spaces. The method iteratively computes Pareto critical points,
    where in each iteration, an approximation of the subdifferential is computed in
    an efficient manner and then used to compute a common descent direction for all
    objective functions. To prove convergence, we present some new optimality results
    for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these,
    we can show that every accumulation point of the sequence generated by our algorithm
    is Pareto critical under common assumptions. Computational efficiency for finding
    Pareto critical points is numerically demonstrated for multiobjective optimal
    control of an obstacle problem.
author:
- first_name: Konstantin
  full_name: Sonntag, Konstantin
  id: '56399'
  last_name: Sonntag
  orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Bennet
  full_name: Gebken, Bennet
  id: '32643'
  last_name: Gebken
- first_name: Georg
  full_name: Müller, Georg
  last_name: Müller
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: 0000-0002-3389-793X
- first_name: Stefan
  full_name: Volkwein, Stefan
  last_name: Volkwein
citation:
  ama: Sonntag K, Gebken B, Müller G, Peitz S, Volkwein S. A Descent Method for Nonsmooth
    Multiobjective Optimization in Hilbert Spaces. <i>arXiv:240206376</i>. Published
    online 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>.
  bibtex: '@article{Sonntag_Gebken_Müller_Peitz_Volkwein_2024, title={A Descent Method
    for Nonsmooth Multiobjective Optimization in Hilbert Spaces}, journal={arXiv:2402.06376},
    author={Sonntag, Konstantin and Gebken, Bennet and Müller, Georg and Peitz, Sebastian
    and Volkwein, Stefan}, year={2024} }'
  chicago: Sonntag, Konstantin, Bennet Gebken, Georg Müller, Sebastian Peitz, and
    Stefan Volkwein. “A Descent Method for Nonsmooth Multiobjective Optimization in
    Hilbert Spaces.” <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.
  mla: Sonntag, Konstantin, et al. “A Descent Method for Nonsmooth Multiobjective
    Optimization in Hilbert Spaces.” <i>ArXiv:2402.06376</i>, 2024.
  short: K. Sonntag, B. Gebken, G. Müller, S. Peitz, S. Volkwein, ArXiv:2402.06376
    (2024).
date_created: 2024-02-13T09:35:26Z
date_updated: 2024-02-21T10:21:03Z
department:
- _id: '101'
- _id: '655'
external_id:
  arxiv:
  - "\t2402.06376"
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2402.06376
oa: '1'
publication: arXiv:2402.06376
status: public
title: A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces
type: preprint
user_id: '56399'
year: '2024'
...
---
_id: '52726'
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.
article_type: original
author:
- first_name: Christian
  full_name: Bick, Christian
  last_name: Bick
- first_name: Sören
  full_name: von der Gracht, Sören
  id: '97359'
  last_name: von der Gracht
  orcid: 0000-0002-8054-2058
citation:
  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>
  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}
    }'
  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>.
  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>.'
  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>.
  short: C. Bick, S. von der Gracht, Journal of Complex Networks 12 (2024).
date_created: 2024-03-22T09:04:57Z
date_updated: 2024-03-22T09:11:53Z
ddc:
- '510'
department:
- _id: '101'
doi: 10.1093/comnet/cnae009
external_id:
  arxiv:
  - '2309.02006'
file:
- access_level: closed
  content_type: application/pdf
  creator: svdg
  date_created: 2024-03-22T09:06:07Z
  date_updated: 2024-03-22T09:06:07Z
  file_id: '52728'
  file_name: heteroclinic-dynamics-in-network-dynamical-systems-with-higher-order-interactions.pdf
  file_size: 649155
  relation: main_file
  success: 1
file_date_updated: 2024-03-22T09:06:07Z
has_accepted_license: '1'
intvolume: '        12'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
- Management Science and Operations Research
- Computer Networks and Communications
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://academic.oup.com/comnet/article-pdf/12/2/cnae009/56832119/cnae009.pdf
oa: '1'
publication: Journal of Complex Networks
publication_identifier:
  issn:
  - 2051-1329
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Heteroclinic dynamics in network dynamical systems with higher-order interactions
type: journal_article
user_id: '97359'
volume: 12
year: '2024'
...
---
_id: '49905'
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 \x03 = 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."
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
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Isaak Hieronymus
  full_name: Wolf, Isaak Hieronymus
  id: '88145'
  last_name: Wolf
citation:
  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>
  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>
  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} }'
  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>.'
  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>.
  short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 44 (2024) 429–440.
date_created: 2023-12-20T10:31:27Z
date_updated: 2024-03-22T12:11:35Z
department:
- _id: '542'
doi: 10.1007/s00493-023-00078-9
intvolume: '        44'
keyword:
- Computational Mathematics
- Discrete Mathematics and Combinatorics
language:
- iso: eng
page: 429-440
publication: Combinatorica
publication_identifier:
  issn:
  - 0209-9683
  - 1439-6912
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs
type: journal_article
user_id: '15540'
volume: 44
year: '2024'
...
---
_id: '53101'
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.
article_type: original
author:
- first_name: Sigrid
  full_name: Leyendecker, Sigrid
  last_name: Leyendecker
- first_name: Sofya
  full_name: Maslovskaya, Sofya
  id: '87909'
  last_name: Maslovskaya
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  id: '16494'
  last_name: Ober-Blöbaum
- first_name: Rodrigo T. Sato Martín de
  full_name: Almagro, Rodrigo T. Sato Martín de
  last_name: Almagro
- first_name: Flóra Orsolya
  full_name: Szemenyei, Flóra Orsolya
  last_name: Szemenyei
citation:
  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>
  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>
  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} }'
  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>.'
  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>.
  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.
date_created: 2024-03-28T15:58:02Z
date_updated: 2024-03-28T16:07:34Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.3934/jcd.2024017
has_accepted_license: '1'
issue: '0'
keyword:
- Optimal control problem
- Lagrangian system
- Hamiltonian system
- Variations
- Pontryagin's maximum principle.
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://www.aimsciences.org/article/doi/10.3934/jcd.2024017
oa: '1'
page: 0-0
publication: Journal of Computational Dynamics
publication_identifier:
  issn:
  - 2158-2491
  - 2158-2505
publication_status: published
publisher: American Institute of Mathematical Sciences (AIMS)
status: public
title: A new Lagrangian approach to control affine systems with a quadratic Lagrange
  term
type: journal_article
user_id: '87909'
volume: '0'
year: '2024'
...
---
_id: '53534'
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."
author:
- first_name: Alena
  full_name: Ernst, Alena
  id: '46953'
  last_name: Ernst
- first_name: Kai-Uwe
  full_name: Schmidt, Kai-Uwe
  last_name: Schmidt
citation:
  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>
  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>
  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} }'
  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>.
  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>.'
  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>.
  short: A. Ernst, K.-U. Schmidt, Mathematische Zeitschrift 307 (2024).
date_created: 2024-04-17T12:26:51Z
date_updated: 2024-06-17T10:04:29Z
department:
- _id: '100'
doi: 10.1007/s00209-024-03511-x
intvolume: '       307'
issue: '45'
language:
- iso: eng
publication: Mathematische Zeitschrift
status: public
title: Transitivity in finite general linear groups
type: journal_article
user_id: '46953'
volume: 307
year: '2024'
...
---
_id: '32447'
abstract:
- lang: eng
  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.'
article_type: original
author:
- first_name: Konstantin
  full_name: Sonntag, Konstantin
  id: '56399'
  last_name: Sonntag
  orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: 0000-0002-3389-793X
citation:
  ama: Sonntag K, Peitz S. Fast 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>
  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>
  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} }'
  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>.'
  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>.'
  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.
date_created: 2022-07-28T11:53:02Z
date_updated: 2024-07-02T09:27:39Z
department:
- _id: '101'
- _id: '655'
doi: 10.1137/23M1588512
intvolume: '        34'
issue: '3'
keyword:
- multiobjective optimization
- Pareto optimization
- Lyapunov analysis
- gradient-likedynamical systems
- inertial dynamics
- asymptotic vanishing damping
- fast convergence
language:
- iso: eng
page: 2259 - 2286
publication: SIAM Journal on Optimization
publication_identifier:
  issn:
  - 1095-7189
publication_status: published
publisher: Society for Industrial and Applied Mathematics
status: public
title: Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic
  Vanishing Damping
type: journal_article
user_id: '56399'
volume: 34
year: '2024'
...
---
_id: '55276'
author:
- first_name: P.
  full_name: Minelli, P.
  last_name: Minelli
- first_name: A.
  full_name: Sourmelidis, A.
  last_name: Sourmelidis
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
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>
  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>
  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} }'
  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>.'
  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.
date_created: 2024-07-16T11:09:00Z
date_updated: 2024-07-24T07:23:20Z
department:
- _id: '102'
doi: 10.1093/imrn/rnad283
intvolume: '      2024'
issue: '10'
language:
- iso: eng
page: 8485–8502
publication: Int. Math. Res. Not. IMRN
status: public
title: On restricted averages of Dedekind sums
type: journal_article
user_id: '106108'
volume: 2024
year: '2024'
...
---
_id: '55278'
author:
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
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>
  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>
  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} }'
  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>.'
  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>.'
  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>.
  short: M. Technau, Proc. Amer. Math. Soc. 152 (2024) 63–69.
date_created: 2024-07-16T11:09:01Z
date_updated: 2024-07-24T07:26:12Z
department:
- _id: '102'
doi: 10.1090/proc/16520
extern: '1'
intvolume: '       152'
issue: '1'
language:
- iso: eng
page: 63–69
publication: Proc. Amer. Math. Soc.
status: public
title: Remark on the Farey fraction spin chain
type: journal_article
user_id: '106108'
volume: 152
year: '2024'
...
---
_id: '46469'
abstract:
- lang: eng
  text: 'We show how to learn discrete field theories from observational data of fields
    on a space-time lattice. For this, we train a neural network model of a discrete
    Lagrangian density such that the discrete Euler--Lagrange equations are consistent
    with the given training data. We, thus, obtain a structure-preserving machine
    learning architecture. Lagrangian densities are not uniquely defined by the solutions
    of a field theory. We introduce a technique to derive regularisers for the training
    process which optimise numerical regularity of the discrete field theory. Minimisation
    of the regularisers guarantees that close to the training data the discrete field
    theory behaves robust and efficient when used in numerical simulations. Further,
    we show how to identify structurally simple solutions of the underlying continuous
    field theory such as travelling waves. This is possible even when travelling waves
    are not present in the training data. This is compared to data-driven model order
    reduction based approaches, which struggle to identify suitable latent spaces
    containing structurally simple solutions when these are not present in the training
    data. Ideas are demonstrated on examples based on the wave equation and the Schrödinger
    equation. '
article_number: '013104'
article_type: original
author:
- first_name: Christian
  full_name: Offen, Christian
  id: '85279'
  last_name: Offen
  orcid: 0000-0002-5940-8057
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  id: '16494'
  last_name: Ober-Blöbaum
citation:
  ama: Offen C, Ober-Blöbaum S. Learning of discrete models of variational PDEs from
    data. <i>Chaos</i>. 2024;34(1). 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>
  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} }'
  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>.
  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>.'
  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>.
  short: C. Offen, S. Ober-Blöbaum, Chaos 34 (2024).
date_created: 2023-08-10T08:24:48Z
date_updated: 2024-08-12T13:45:43Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1063/5.0172287
external_id:
  arxiv:
  - '2308.05082 '
file:
- access_level: open_access
  content_type: application/pdf
  creator: coffen
  date_created: 2024-01-09T10:48:38Z
  date_updated: 2024-01-09T10:48:38Z
  file_id: '50376'
  file_name: Accepted manuscript with AIP banner CHA23-AR-01370.pdf
  file_size: 13222105
  relation: main_file
  title: Accepted Manuscript Chaos
- access_level: open_access
  content_type: application/pdf
  creator: coffen
  date_created: 2024-01-09T11:19:49Z
  date_updated: 2024-01-09T11:19:49Z
  description: |-
    We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train
    a neural network model of a discrete Lagrangian density such that the discrete Euler–Lagrange equations are consistent
    with the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian
    densities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for
    the training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers
    guarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical
    simulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory
    such as travelling waves. This is possible even when travelling waves are not present in the training data. This is
    compared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces
    containing structurally simple solutions when these are not present in the training data. Ideas are demonstrated on
    examples based on the wave equation and the Schrödinger equation.
  file_id: '50390'
  file_name: LDensityPDE_AIP.pdf
  file_size: 12960884
  relation: main_file
  title: Learning of discrete models of variational PDEs from data
file_date_updated: 2024-01-09T11:19:49Z
has_accepted_license: '1'
intvolume: '        34'
issue: '1'
language:
- iso: eng
oa: '1'
project:
- _id: '52'
  name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: Chaos
publication_identifier:
  issn:
  - 1054-1500
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
related_material:
  link:
  - description: GitHub
    relation: software
    url: https://github.com/Christian-Offen/DLNN_pde
status: public
title: Learning of discrete models of variational PDEs from data
type: journal_article
user_id: '85279'
volume: 34
year: '2024'
...