---
_id: '32097'
author:
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Yannick
full_name: Guedes Bonthonneau, Yannick
last_name: Guedes Bonthonneau
- first_name: Colin
full_name: Guillarmou, Colin
last_name: Guillarmou
citation:
ama: Weich T, Guedes Bonthonneau Y, Guillarmou C. SRB Measures of Anosov Actions.
Journal of Differential Geometry (to appear) -- arXiv:210312127. Published
online 2024.
apa: Weich, T., Guedes Bonthonneau, Y., & Guillarmou, C. (2024). SRB Measures
of Anosov Actions. Journal of Differential Geometry (to Appear) -- ArXiv:2103.12127.
bibtex: '@article{Weich_Guedes Bonthonneau_Guillarmou_2024, title={SRB Measures
of Anosov Actions}, journal={Journal of Differential Geometry (to appear) --
arXiv:2103.12127}, author={Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou,
Colin}, year={2024} }'
chicago: Weich, Tobias, Yannick Guedes Bonthonneau, and Colin Guillarmou. “SRB Measures
of Anosov Actions.” Journal of Differential Geometry (to Appear) -- ArXiv:2103.12127,
2024.
ieee: T. Weich, Y. Guedes Bonthonneau, and C. Guillarmou, “SRB Measures of Anosov
Actions,” Journal of Differential Geometry (to appear) -- arXiv:2103.12127,
2024.
mla: Weich, Tobias, et al. “SRB Measures of Anosov Actions.” Journal of Differential
Geometry (to Appear) -- ArXiv:2103.12127, 2024.
short: T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, Journal of Differential Geometry
(to Appear) -- ArXiv:2103.12127 (2024).
date_created: 2022-06-22T09:56:23Z
date_updated: 2023-12-21T09:47:22Z
ddc:
- '510'
department:
- _id: '10'
- _id: '623'
- _id: '548'
external_id:
arxiv:
- https://arxiv.org/abs/2103.12127
file:
- access_level: open_access
content_type: application/pdf
creator: weich
date_created: 2022-06-22T09:56:08Z
date_updated: 2022-06-22T09:56:08Z
file_id: '32098'
file_name: 2103.12127.pdf
file_size: 745870
relation: main_file
file_date_updated: 2022-06-22T09:56:08Z
has_accepted_license: '1'
language:
- iso: eng
oa: '1'
publication: Journal of Differential Geometry (to appear) -- arXiv:2103.12127
status: public
title: SRB Measures of Anosov Actions
type: journal_article
user_id: '49178'
year: '2024'
...
---
_id: '46469'
abstract:
- lang: eng
text: 'We show how to learn discrete field theories from observational data of fields
on a space-time lattice. For this, we train a neural network model of a discrete
Lagrangian density such that the discrete Euler--Lagrange equations are consistent
with the given training data. We, thus, obtain a structure-preserving machine
learning architecture. Lagrangian densities are not uniquely defined by the solutions
of a field theory. We introduce a technique to derive regularisers for the training
process which optimise numerical regularity of the discrete field theory. Minimisation
of the regularisers guarantees that close to the training data the discrete field
theory behaves robust and efficient when used in numerical simulations. Further,
we show how to identify structurally simple solutions of the underlying continuous
field theory such as travelling waves. This is possible even when travelling waves
are not present in the training data. This is compared to data-driven model order
reduction based approaches, which struggle to identify suitable latent spaces
containing structurally simple solutions when these are not present in the training
data. Ideas are demonstrated on examples based on the wave equation and the Schrödinger
equation. '
article_number: '013104'
article_type: original
author:
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: Offen C, Ober-Blöbaum S. Learning of discrete models of variational PDEs from
data. Chaos. 2024;34(1). doi:10.1063/5.0172287
apa: Offen, C., & Ober-Blöbaum, S. (2024). Learning of discrete models of variational
PDEs from data. Chaos, 34(1), Article 013104. https://doi.org/10.1063/5.0172287
bibtex: '@article{Offen_Ober-Blöbaum_2024, title={Learning of discrete models of
variational PDEs from data}, volume={34}, DOI={10.1063/5.0172287},
number={1013104}, journal={Chaos}, publisher={AIP Publishing}, author={Offen,
Christian and Ober-Blöbaum, Sina}, year={2024} }'
chicago: Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of
Variational PDEs from Data.” Chaos 34, no. 1 (2024). https://doi.org/10.1063/5.0172287.
ieee: 'C. Offen and S. Ober-Blöbaum, “Learning of discrete models of variational
PDEs from data,” Chaos, vol. 34, no. 1, Art. no. 013104, 2024, doi: 10.1063/5.0172287.'
mla: Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational
PDEs from Data.” Chaos, vol. 34, no. 1, 013104, AIP Publishing, 2024, doi:10.1063/5.0172287.
short: C. Offen, S. Ober-Blöbaum, Chaos 34 (2024).
date_created: 2023-08-10T08:24:48Z
date_updated: 2024-01-09T11:29:06Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1063/5.0172287
external_id:
arxiv:
- '2308.05082 '
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2024-01-09T10:48:38Z
date_updated: 2024-01-09T10:48:38Z
file_id: '50376'
file_name: Accepted manuscript with AIP banner CHA23-AR-01370.pdf
file_size: 13222105
relation: main_file
title: Accepted Manuscript Chaos
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2024-01-09T11:19:49Z
date_updated: 2024-01-09T11:19:49Z
description: |-
We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train
a neural network model of a discrete Lagrangian density such that the discrete Euler–Lagrange equations are consistent
with the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian
densities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for
the training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers
guarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical
simulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory
such as travelling waves. This is possible even when travelling waves are not present in the training data. This is
compared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces
containing structurally simple solutions when these are not present in the training data. Ideas are demonstrated on
examples based on the wave equation and the Schrödinger equation.
file_id: '50390'
file_name: LDensityPDE_AIP.pdf
file_size: 12960884
relation: main_file
title: Learning of discrete models of variational PDEs from data
file_date_updated: 2024-01-09T11:19:49Z
has_accepted_license: '1'
intvolume: ' 34'
issue: '1'
language:
- iso: eng
oa: '1'
publication: Chaos
publication_identifier:
issn:
- 1054-1500
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/Christian-Offen/DLNN_pde
status: public
title: Learning of discrete models of variational PDEs from data
type: journal_article
user_id: '85279'
volume: 34
year: '2024'
...
---
_id: '50554'
author:
- first_name: Susanne
full_name: Prediger, Susanne
last_name: Prediger
- first_name: Lena
full_name: Wessel, Lena
id: '85190'
last_name: Wessel
citation:
ama: 'Prediger S, Wessel L. 31 Sprachbildung im berufsbezogenen Mathematikunterricht.
In: Efing C, Kalkavan-Aydin Z, eds. Berufs-und Fachsprache Deutsch in Wissenschaft
und Praxis. Vol Band 3. DaZ-Handbücher. DE GRUYTER; 2024:363-372.'
apa: 'Prediger, S., & Wessel, L. (2024). 31 Sprachbildung im berufsbezogenen
Mathematikunterricht. In C. Efing & Z. Kalkavan-Aydin (Eds.), Berufs-und
Fachsprache Deutsch in Wissenschaft und Praxis: Vol. Band 3 (pp. 363–372).
DE GRUYTER.'
bibtex: '@inbook{Prediger_Wessel_2024, place={Berlin}, series={DaZ-Handbücher},
title={31 Sprachbildung im berufsbezogenen Mathematikunterricht.}, volume={Band
3}, booktitle={Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis}, publisher={DE
GRUYTER}, author={Prediger, Susanne and Wessel, Lena}, editor={Efing, Christian
and Kalkavan-Aydin, Zeynep}, year={2024}, pages={363–372}, collection={DaZ-Handbücher}
}'
chicago: 'Prediger, Susanne, and Lena Wessel. “31 Sprachbildung im berufsbezogenen
Mathematikunterricht.” In Berufs-und Fachsprache Deutsch in Wissenschaft und
Praxis, edited by Christian Efing and Zeynep Kalkavan-Aydin, Band 3:363–72.
DaZ-Handbücher. Berlin: DE GRUYTER, 2024.'
ieee: 'S. Prediger and L. Wessel, “31 Sprachbildung im berufsbezogenen Mathematikunterricht.,”
in Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis, vol. Band
3, C. Efing and Z. Kalkavan-Aydin, Eds. Berlin: DE GRUYTER, 2024, pp. 363–372.'
mla: Prediger, Susanne, and Lena Wessel. “31 Sprachbildung im berufsbezogenen Mathematikunterricht.”
Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis, edited by Christian
Efing and Zeynep Kalkavan-Aydin, vol. Band 3, DE GRUYTER, 2024, pp. 363–72.
short: 'S. Prediger, L. Wessel, in: C. Efing, Z. Kalkavan-Aydin (Eds.), Berufs-und
Fachsprache Deutsch in Wissenschaft und Praxis, DE GRUYTER, Berlin, 2024, pp.
363–372.'
date_created: 2024-01-17T10:58:04Z
date_updated: 2024-01-17T11:07:21Z
department:
- _id: '34'
- _id: '10'
- _id: '643'
editor:
- first_name: Christian
full_name: Efing, Christian
last_name: Efing
- first_name: Zeynep
full_name: Kalkavan-Aydin, Zeynep
last_name: Kalkavan-Aydin
language:
- iso: ger
main_file_link:
- open_access: '1'
url: https://www.degruyter.com/document/doi/10.1515/9783110745504/pdf?licenseType=restricted#page=381
oa: '1'
page: 363-372
place: Berlin
publication: Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis
publication_identifier:
isbn:
- 978-3-11-074544-3
publication_status: published
publisher: DE GRUYTER
series_title: DaZ-Handbücher
status: public
title: 31 Sprachbildung im berufsbezogenen Mathematikunterricht.
type: book_chapter
user_id: '37888'
volume: Band 3
year: '2024'
...
---
_id: '51208'
abstract:
- lang: eng
text: AbstractApproximation of subdifferentials
is one of the main tasks when computing descent directions for nonsmooth optimization
problems. In this article, we propose a bisection method for weakly lower semismooth
functions which is able to compute new subgradients that improve a given approximation
in case a direction with insufficient descent was computed. Combined with a recently
proposed deterministic gradient sampling approach, this yields a deterministic
and provably convergent way to approximate subdifferentials for computing descent
directions.
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
citation:
ama: Gebken B. A note on the convergence of deterministic gradient sampling in nonsmooth
optimization. Computational Optimization and Applications. Published online
2024. doi:10.1007/s10589-024-00552-0
apa: Gebken, B. (2024). A note on the convergence of deterministic gradient sampling
in nonsmooth optimization. Computational Optimization and Applications.
https://doi.org/10.1007/s10589-024-00552-0
bibtex: '@article{Gebken_2024, title={A note on the convergence of deterministic
gradient sampling in nonsmooth optimization}, DOI={10.1007/s10589-024-00552-0},
journal={Computational Optimization and Applications}, publisher={Springer Science
and Business Media LLC}, author={Gebken, Bennet}, year={2024} }'
chicago: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling
in Nonsmooth Optimization.” Computational Optimization and Applications,
2024. https://doi.org/10.1007/s10589-024-00552-0.
ieee: 'B. Gebken, “A note on the convergence of deterministic gradient sampling
in nonsmooth optimization,” Computational Optimization and Applications,
2024, doi: 10.1007/s10589-024-00552-0.'
mla: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling
in Nonsmooth Optimization.” Computational Optimization and Applications,
Springer Science and Business Media LLC, 2024, doi:10.1007/s10589-024-00552-0.
short: B. Gebken, Computational Optimization and Applications (2024).
date_created: 2024-02-07T07:23:23Z
date_updated: 2024-02-08T08:05:54Z
department:
- _id: '101'
doi: 10.1007/s10589-024-00552-0
keyword:
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
language:
- iso: eng
publication: Computational Optimization and Applications
publication_identifier:
issn:
- 0926-6003
- 1573-2894
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: A note on the convergence of deterministic gradient sampling in nonsmooth optimization
type: journal_article
user_id: '32643'
year: '2024'
...
---
_id: '51204'
abstract:
- lang: eng
text: "Given a real semisimple connected Lie group $G$ and a discrete torsion-free\r\nsubgroup
$\\Gamma < G$ we prove a precise connection between growth rates of the\r\ngroup
$\\Gamma$, polyhedral bounds on the joint spectrum of the ring of\r\ninvariant
differential operators, and the decay of matrix coefficients. In\r\nparticular,
this allows us to completely characterize temperedness of\r\n$L^2(\\Gamma\\backslash
G)$ in this general setting."
author:
- first_name: Christopher
full_name: Lutsko, Christopher
last_name: Lutsko
- first_name: Tobias
full_name: Weich, Tobias
last_name: Weich
- first_name: Lasse Lennart
full_name: Wolf, Lasse Lennart
id: '45027'
last_name: Wolf
citation:
ama: Lutsko C, Weich T, Wolf LL. Polyhedral bounds on the joint spectrum and temperedness
of locally symmetric spaces. arXiv:240202530. Published online 2024.
apa: Lutsko, C., Weich, T., & Wolf, L. L. (2024). Polyhedral bounds on the joint
spectrum and temperedness of locally symmetric spaces. In arXiv:2402.02530.
bibtex: '@article{Lutsko_Weich_Wolf_2024, title={Polyhedral bounds on the joint
spectrum and temperedness of locally symmetric spaces}, journal={arXiv:2402.02530},
author={Lutsko, Christopher and Weich, Tobias and Wolf, Lasse Lennart}, year={2024}
}'
chicago: Lutsko, Christopher, Tobias Weich, and Lasse Lennart Wolf. “Polyhedral
Bounds on the Joint Spectrum and Temperedness of Locally Symmetric Spaces.” ArXiv:2402.02530,
2024.
ieee: C. Lutsko, T. Weich, and L. L. Wolf, “Polyhedral bounds on the joint spectrum
and temperedness of locally symmetric spaces,” arXiv:2402.02530. 2024.
mla: Lutsko, Christopher, et al. “Polyhedral Bounds on the Joint Spectrum and Temperedness
of Locally Symmetric Spaces.” ArXiv:2402.02530, 2024.
short: C. Lutsko, T. Weich, L.L. Wolf, ArXiv:2402.02530 (2024).
date_created: 2024-02-06T20:35:36Z
date_updated: 2024-02-11T19:56:35Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
external_id:
arxiv:
- '2402.02530'
language:
- iso: eng
publication: arXiv:2402.02530
status: public
title: Polyhedral bounds on the joint spectrum and temperedness of locally symmetric
spaces
type: preprint
user_id: '49178'
year: '2024'
...
---
_id: '51374'
article_number: '110319'
author:
- first_name: David
full_name: Hasler, David
last_name: Hasler
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Oliver
full_name: Siebert, Oliver
last_name: Siebert
citation:
ama: Hasler D, Hinrichs B, Siebert O. Non-Fock ground states in the translation-invariant
Nelson model revisited non-perturbatively. Journal of Functional Analysis.
2024;286(7). doi:10.1016/j.jfa.2024.110319
apa: Hasler, D., Hinrichs, B., & Siebert, O. (2024). Non-Fock ground states
in the translation-invariant Nelson model revisited non-perturbatively. Journal
of Functional Analysis, 286(7), Article 110319. https://doi.org/10.1016/j.jfa.2024.110319
bibtex: '@article{Hasler_Hinrichs_Siebert_2024, title={Non-Fock ground states in
the translation-invariant Nelson model revisited non-perturbatively}, volume={286},
DOI={10.1016/j.jfa.2024.110319},
number={7110319}, journal={Journal of Functional Analysis}, publisher={Elsevier
BV}, author={Hasler, David and Hinrichs, Benjamin and Siebert, Oliver}, year={2024}
}'
chicago: Hasler, David, Benjamin Hinrichs, and Oliver Siebert. “Non-Fock Ground
States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively.”
Journal of Functional Analysis 286, no. 7 (2024). https://doi.org/10.1016/j.jfa.2024.110319.
ieee: 'D. Hasler, B. Hinrichs, and O. Siebert, “Non-Fock ground states in the translation-invariant
Nelson model revisited non-perturbatively,” Journal of Functional Analysis,
vol. 286, no. 7, Art. no. 110319, 2024, doi: 10.1016/j.jfa.2024.110319.'
mla: Hasler, David, et al. “Non-Fock Ground States in the Translation-Invariant
Nelson Model Revisited Non-Perturbatively.” Journal of Functional Analysis,
vol. 286, no. 7, 110319, Elsevier BV, 2024, doi:10.1016/j.jfa.2024.110319.
short: D. Hasler, B. Hinrichs, O. Siebert, Journal of Functional Analysis 286 (2024).
date_created: 2024-02-18T12:31:28Z
date_updated: 2024-02-18T12:32:23Z
department:
- _id: '799'
doi: 10.1016/j.jfa.2024.110319
extern: '1'
external_id:
arxiv:
- '2302.06998'
intvolume: ' 286'
issue: '7'
keyword:
- Analysis
language:
- iso: eng
publication: Journal of Functional Analysis
publication_identifier:
issn:
- 0022-1236
publication_status: published
publisher: Elsevier BV
status: public
title: Non-Fock ground states in the translation-invariant Nelson model revisited
non-perturbatively
type: journal_article
user_id: '99427'
volume: 286
year: '2024'
...
---
_id: '32101'
author:
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Yannick
full_name: Guedes Bonthonneau, Yannick
last_name: Guedes Bonthonneau
- first_name: Colin
full_name: Guillarmou, Colin
last_name: Guillarmou
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
citation:
ama: Weich T, Guedes Bonthonneau Y, Guillarmou C, Hilgert J. Ruelle-Taylor resonaces
of Anosov actions. J Europ Math Soc. Published online 2024:1-36.
apa: Weich, T., Guedes Bonthonneau, Y., Guillarmou, C., & Hilgert, J. (2024).
Ruelle-Taylor resonaces of Anosov actions. J. Europ. Math. Soc., 1–36.
bibtex: '@article{Weich_Guedes Bonthonneau_Guillarmou_Hilgert_2024, title={Ruelle-Taylor
resonaces of Anosov actions}, journal={J. Europ. Math. Soc.}, author={Weich, Tobias
and Guedes Bonthonneau, Yannick and Guillarmou, Colin and Hilgert, Joachim}, year={2024},
pages={1–36} }'
chicago: Weich, Tobias, Yannick Guedes Bonthonneau, Colin Guillarmou, and Joachim
Hilgert. “Ruelle-Taylor Resonaces of Anosov Actions.” J. Europ. Math. Soc.,
2024, 1–36.
ieee: T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, and J. Hilgert, “Ruelle-Taylor
resonaces of Anosov actions,” J. Europ. Math. Soc., pp. 1–36, 2024.
mla: Weich, Tobias, et al. “Ruelle-Taylor Resonaces of Anosov Actions.” J. Europ.
Math. Soc., 2024, pp. 1–36.
short: T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, J. Hilgert, J. Europ. Math.
Soc. (2024) 1–36.
date_created: 2022-06-22T09:56:51Z
date_updated: 2024-02-19T06:25:13Z
ddc:
- '510'
department:
- _id: '10'
- _id: '623'
- _id: '548'
- _id: '91'
file:
- access_level: open_access
content_type: application/pdf
creator: weich
date_created: 2022-06-22T09:56:47Z
date_updated: 2022-06-22T09:56:47Z
file_id: '32102'
file_name: 2007.14275.pdf
file_size: 796410
relation: main_file
file_date_updated: 2022-06-22T09:56:47Z
has_accepted_license: '1'
language:
- iso: eng
oa: '1'
page: 1-36
publication: J. Europ. Math. Soc.
publication_status: published
status: public
title: Ruelle-Taylor resonaces of Anosov actions
type: journal_article
user_id: '49063'
year: '2024'
...
---
_id: '51501'
author:
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
citation:
ama: Hilgert J. Quantum-Classical Correspondences for Locally Symmetric Spaces.
Published online 2024.
apa: Hilgert, J. (2024). Quantum-Classical Correspondences for Locally Symmetric
Spaces.
bibtex: '@article{Hilgert_2024, title={Quantum-Classical Correspondences for Locally
Symmetric Spaces}, author={Hilgert, Joachim}, year={2024} }'
chicago: Hilgert, Joachim. “Quantum-Classical Correspondences for Locally Symmetric
Spaces,” 2024.
ieee: J. Hilgert, “Quantum-Classical Correspondences for Locally Symmetric Spaces.”
2024.
mla: Hilgert, Joachim. Quantum-Classical Correspondences for Locally Symmetric
Spaces. 2024.
short: J. Hilgert, (2024).
date_created: 2024-02-19T10:31:51Z
date_updated: 2024-02-19T10:32:07Z
department:
- _id: '91'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2303.00578.pdf
oa: '1'
publication_status: published
status: public
title: Quantum-Classical Correspondences for Locally Symmetric Spaces
type: preprint
user_id: '49063'
year: '2024'
...
---
_id: '46019'
abstract:
- lang: eng
text: We derive efficient algorithms to compute weakly Pareto optimal solutions
for smooth, convex and unconstrained multiobjective optimization problems in general
Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical
system in the multiobjective setting, which trajectories converge weakly to Pareto
optimal solutions. Discretization of this system yields an inertial multiobjective
algorithm which generates sequences that converge weakly to Pareto optimal solutions.
We employ Nesterov acceleration to define an algorithm with an improved convergence
rate compared to the plain multiobjective steepest descent method (Algorithm 1).
A further improvement in terms of efficiency is achieved by avoiding the solution
of a quadratic subproblem to compute a common step direction for all objective
functions, which is usually required in first-order methods. Using a different
discretization of our inertial gradient-like dynamical system, we obtain an accelerated
multiobjective gradient method that does not require the solution of a subproblem
in each step (Algorithm 2). While this algorithm does not converge in general,
it yields good results on test problems while being faster than standard steepest
descent.
author:
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Sonntag K, Peitz S. Fast Multiobjective Gradient Methods with Nesterov Acceleration
via Inertial Gradient-Like Systems. Journal of Optimization Theory and Applications.
Published online 2024. doi:10.1007/s10957-024-02389-3
apa: Sonntag, K., & Peitz, S. (2024). Fast Multiobjective Gradient Methods with
Nesterov Acceleration via Inertial Gradient-Like Systems. Journal of Optimization
Theory and Applications. https://doi.org/10.1007/s10957-024-02389-3
bibtex: '@article{Sonntag_Peitz_2024, title={Fast Multiobjective Gradient Methods
with Nesterov Acceleration via Inertial Gradient-Like Systems}, DOI={10.1007/s10957-024-02389-3},
journal={Journal of Optimization Theory and Applications}, publisher={Springer},
author={Sonntag, Konstantin and Peitz, Sebastian}, year={2024} }'
chicago: Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient
Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal
of Optimization Theory and Applications, 2024. https://doi.org/10.1007/s10957-024-02389-3.
ieee: 'K. Sonntag and S. Peitz, “Fast Multiobjective Gradient Methods with Nesterov
Acceleration via Inertial Gradient-Like Systems,” Journal of Optimization Theory
and Applications, 2024, doi: 10.1007/s10957-024-02389-3.'
mla: Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods
with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal of
Optimization Theory and Applications, Springer, 2024, doi:10.1007/s10957-024-02389-3.
short: K. Sonntag, S. Peitz, Journal of Optimization Theory and Applications (2024).
date_created: 2023-07-12T06:35:58Z
date_updated: 2024-02-21T10:13:33Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/s10957-024-02389-3
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s10957-024-02389-3.pdf
oa: '1'
publication: Journal of Optimization Theory and Applications
publication_status: published
publisher: Springer
status: public
title: Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial
Gradient-Like Systems
type: journal_article
user_id: '56399'
year: '2024'
...
---
_id: '51334'
abstract:
- lang: eng
text: The efficient optimization method for locally Lipschitz continuous multiobjective
optimization problems from [1] is extended from finite-dimensional problems to
general Hilbert spaces. The method iteratively computes Pareto critical points,
where in each iteration, an approximation of the subdifferential is computed in
an efficient manner and then used to compute a common descent direction for all
objective functions. To prove convergence, we present some new optimality results
for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these,
we can show that every accumulation point of the sequence generated by our algorithm
is Pareto critical under common assumptions. Computational efficiency for finding
Pareto critical points is numerically demonstrated for multiobjective optimal
control of an obstacle problem.
author:
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Georg
full_name: Müller, Georg
last_name: Müller
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Stefan
full_name: Volkwein, Stefan
last_name: Volkwein
citation:
ama: Sonntag K, Gebken B, Müller G, Peitz S, Volkwein S. A Descent Method for Nonsmooth
Multiobjective Optimization in Hilbert Spaces. arXiv:240206376. Published
online 2024.
apa: Sonntag, K., Gebken, B., Müller, G., Peitz, S., & Volkwein, S. (2024).
A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.
In arXiv:2402.06376.
bibtex: '@article{Sonntag_Gebken_Müller_Peitz_Volkwein_2024, title={A Descent Method
for Nonsmooth Multiobjective Optimization in Hilbert Spaces}, journal={arXiv:2402.06376},
author={Sonntag, Konstantin and Gebken, Bennet and Müller, Georg and Peitz, Sebastian
and Volkwein, Stefan}, year={2024} }'
chicago: Sonntag, Konstantin, Bennet Gebken, Georg Müller, Sebastian Peitz, and
Stefan Volkwein. “A Descent Method for Nonsmooth Multiobjective Optimization in
Hilbert Spaces.” ArXiv:2402.06376, 2024.
ieee: K. Sonntag, B. Gebken, G. Müller, S. Peitz, and S. Volkwein, “A Descent Method
for Nonsmooth Multiobjective Optimization in Hilbert Spaces,” arXiv:2402.06376.
2024.
mla: Sonntag, Konstantin, et al. “A Descent Method for Nonsmooth Multiobjective
Optimization in Hilbert Spaces.” ArXiv:2402.06376, 2024.
short: K. Sonntag, B. Gebken, G. Müller, S. Peitz, S. Volkwein, ArXiv:2402.06376
(2024).
date_created: 2024-02-13T09:35:26Z
date_updated: 2024-02-21T10:21:03Z
department:
- _id: '101'
- _id: '655'
external_id:
arxiv:
- "\t2402.06376"
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2402.06376
oa: '1'
publication: arXiv:2402.06376
status: public
title: A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces
type: preprint
user_id: '56399'
year: '2024'
...