---
_id: '57472'
abstract:
- lang: eng
text: In this paper we introduce, in a Hilbert space setting, a second order dynamical
system with asymptotically vanishing damping and vanishing Tikhonov regularization
that approaches a multiobjective optimization problem with convex and differentiable
components of the objective function. Trajectory solutions are shown to exist
in finite dimensions. We prove fast convergence of the function values, quantified
in terms of a merit function. Based on the regime considered, we establish both
weak and, in some cases, strong convergence of trajectory solutions toward a weak
Pareto optimal solution. To achieve this, we apply Tikhonov regularization individually
to each component of the objective function. This work extends results from single
objective convex optimization into the multiobjective setting.
author:
- first_name: Radu Ioan
full_name: Bot, Radu Ioan
last_name: Bot
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
citation:
ama: Bot RI, Sonntag K. Inertial dynamics with vanishing Tikhonov regularization
for multobjective optimization. Journal of Mathematical Analysis and Applications.
Published online 2025.
apa: Bot, R. I., & Sonntag, K. (2025). Inertial dynamics with vanishing Tikhonov
regularization for multobjective optimization. Journal of Mathematical Analysis
and Applications.
bibtex: '@article{Bot_Sonntag_2025, title={Inertial dynamics with vanishing Tikhonov
regularization for multobjective optimization}, journal={Journal of Mathematical
Analysis and Applications}, author={Bot, Radu Ioan and Sonntag, Konstantin}, year={2025}
}'
chicago: Bot, Radu Ioan, and Konstantin Sonntag. “Inertial Dynamics with Vanishing
Tikhonov Regularization for Multobjective Optimization.” Journal of Mathematical
Analysis and Applications, 2025.
ieee: R. I. Bot and K. Sonntag, “Inertial dynamics with vanishing Tikhonov regularization
for multobjective optimization,” Journal of Mathematical Analysis and Applications,
2025.
mla: Bot, Radu Ioan, and Konstantin Sonntag. “Inertial Dynamics with Vanishing Tikhonov
Regularization for Multobjective Optimization.” Journal of Mathematical Analysis
and Applications, 2025.
short: R.I. Bot, K. Sonntag, Journal of Mathematical Analysis and Applications (2025).
date_created: 2024-11-28T08:58:17Z
date_updated: 2025-10-16T11:56:36Z
ddc:
- '510'
department:
- _id: '101'
- _id: '530'
- _id: '655'
external_id:
arxiv:
- '2411.18422'
file:
- access_level: open_access
content_type: application/pdf
creator: sonntagk
date_created: 2024-11-28T08:58:00Z
date_updated: 2024-11-28T08:58:00Z
file_id: '57473'
file_name: Inertial dynamics with vanishing Tikhonov regularization for multobjective
optimization.pdf
file_size: 4291134
relation: main_file
file_date_updated: 2024-11-28T08:58:00Z
has_accepted_license: '1'
keyword:
- Pareto optimization
- Lyapunov analysis
- gradient-like dynamical systems
- inertial dynamics
- asymptotic vanishing damping
- Tikhonov regularization
- strong convergence
language:
- iso: eng
main_file_link:
- url: https://arxiv.org/pdf/2411.18422
oa: '1'
publication: Journal of Mathematical Analysis and Applications
status: public
title: Inertial dynamics with vanishing Tikhonov regularization for multobjective
optimization
type: journal_article
user_id: '56399'
year: '2025'
...
---
_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. SIAM Journal on Optimization.
2024;34(3):2259-2286. doi:10.1137/23M1588512
apa: Sonntag, K., & Peitz, S. (2024). Fast Convergence of Inertial Multiobjective
Gradient-Like Systems with Asymptotic Vanishing Damping. SIAM Journal on Optimization,
34(3), 2259–2286. https://doi.org/10.1137/23M1588512
bibtex: '@article{Sonntag_Peitz_2024, title={Fast Convergence of Inertial Multiobjective
Gradient-Like Systems with Asymptotic Vanishing Damping}, volume={34}, DOI={10.1137/23M1588512}, 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.” SIAM
Journal on Optimization 34, no. 3 (2024): 2259–86. https://doi.org/10.1137/23M1588512.'
ieee: 'K. Sonntag and S. Peitz, “Fast Convergence of Inertial Multiobjective Gradient-Like
Systems with Asymptotic Vanishing Damping,” SIAM Journal on Optimization,
vol. 34, no. 3, pp. 2259–2286, 2024, doi: 10.1137/23M1588512.'
mla: Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial Multiobjective
Gradient-Like Systems with Asymptotic Vanishing Damping.” SIAM Journal on Optimization,
vol. 34, no. 3, Society for Industrial and Applied Mathematics, 2024, pp. 2259–86,
doi:10.1137/23M1588512.
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: '56221'
author:
- first_name: Angel E.
full_name: Rodriguez-Fernandez, Angel E.
last_name: Rodriguez-Fernandez
- first_name: Lennart
full_name: Schäpermeier, Lennart
last_name: Schäpermeier
- first_name: Carlos
full_name: Hernández, Carlos
last_name: Hernández
- first_name: Pascal
full_name: Kerschke, Pascal
last_name: Kerschke
- first_name: Heike
full_name: Trautmann, Heike
id: '100740'
last_name: Trautmann
orcid: 0000-0002-9788-8282
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
citation:
ama: Rodriguez-Fernandez AE, Schäpermeier L, Hernández C, Kerschke P, Trautmann
H, Schütze O. Finding ϵ-Locally Optimal Solutions for Multi-Objective Multimodal
Optimization. IEEE Transactions on Evolutionary Computation. Published
online 2024:1-1. doi:10.1109/TEVC.2024.3458855
apa: Rodriguez-Fernandez, A. E., Schäpermeier, L., Hernández, C., Kerschke, P.,
Trautmann, H., & Schütze, O. (2024). Finding ϵ-Locally Optimal Solutions for
Multi-Objective Multimodal Optimization. IEEE Transactions on Evolutionary
Computation, 1–1. https://doi.org/10.1109/TEVC.2024.3458855
bibtex: '@article{Rodriguez-Fernandez_Schäpermeier_Hernández_Kerschke_Trautmann_Schütze_2024,
title={Finding ϵ-Locally Optimal Solutions for Multi-Objective Multimodal Optimization},
DOI={10.1109/TEVC.2024.3458855},
journal={IEEE Transactions on Evolutionary Computation}, author={Rodriguez-Fernandez,
Angel E. and Schäpermeier, Lennart and Hernández, Carlos and Kerschke, Pascal
and Trautmann, Heike and Schütze, Oliver}, year={2024}, pages={1–1} }'
chicago: Rodriguez-Fernandez, Angel E., Lennart Schäpermeier, Carlos Hernández,
Pascal Kerschke, Heike Trautmann, and Oliver Schütze. “Finding ϵ-Locally Optimal
Solutions for Multi-Objective Multimodal Optimization.” IEEE Transactions on
Evolutionary Computation, 2024, 1–1. https://doi.org/10.1109/TEVC.2024.3458855.
ieee: 'A. E. Rodriguez-Fernandez, L. Schäpermeier, C. Hernández, P. Kerschke, H.
Trautmann, and O. Schütze, “Finding ϵ-Locally Optimal Solutions for Multi-Objective
Multimodal Optimization,” IEEE Transactions on Evolutionary Computation,
pp. 1–1, 2024, doi: 10.1109/TEVC.2024.3458855.'
mla: Rodriguez-Fernandez, Angel E., et al. “Finding ϵ-Locally Optimal Solutions
for Multi-Objective Multimodal Optimization.” IEEE Transactions on Evolutionary
Computation, 2024, pp. 1–1, doi:10.1109/TEVC.2024.3458855.
short: A.E. Rodriguez-Fernandez, L. Schäpermeier, C. Hernández, P. Kerschke, H.
Trautmann, O. Schütze, IEEE Transactions on Evolutionary Computation (2024) 1–1.
date_created: 2024-09-24T08:01:14Z
date_updated: 2024-09-24T08:01:47Z
doi: 10.1109/TEVC.2024.3458855
keyword:
- Optimization
- Evolutionary computation
- Approximation algorithms
- Benchmark testing
- Vectors
- Surveys
- Pareto optimization
- multi-objective optimization
- evolutionary computation
- multimodal optimization
- local solutions
language:
- iso: eng
page: 1-1
publication: IEEE Transactions on Evolutionary Computation
status: public
title: Finding ϵ-Locally Optimal Solutions for Multi-Objective Multimodal Optimization
type: journal_article
user_id: '15504'
year: '2024'
...
---
_id: '63497'
author:
- first_name: Nikolas
full_name: Förster, Nikolas
last_name: Förster
- first_name: Oliver
full_name: Wallscheid, Oliver
last_name: Wallscheid
- first_name: Frank
full_name: Schafmeister, Frank
last_name: Schafmeister
citation:
ama: 'Förster N, Wallscheid O, Schafmeister F. Dual-Active Bridge Sequential Pareto
Optimization for Fast Pre-Design and Final Component Selection. In: 2024 IEEE
Design Methodologies Conference (DMC). ; 2024:1-8. doi:10.1109/DMC62632.2024.10812131'
apa: Förster, N., Wallscheid, O., & Schafmeister, F. (2024). Dual-Active Bridge
Sequential Pareto Optimization for Fast Pre-Design and Final Component Selection.
2024 IEEE Design Methodologies Conference (DMC), 1–8. https://doi.org/10.1109/DMC62632.2024.10812131
bibtex: '@inproceedings{Förster_Wallscheid_Schafmeister_2024, title={Dual-Active
Bridge Sequential Pareto Optimization for Fast Pre-Design and Final Component
Selection}, DOI={10.1109/DMC62632.2024.10812131},
booktitle={2024 IEEE Design Methodologies Conference (DMC)}, author={Förster,
Nikolas and Wallscheid, Oliver and Schafmeister, Frank}, year={2024}, pages={1–8}
}'
chicago: Förster, Nikolas, Oliver Wallscheid, and Frank Schafmeister. “Dual-Active
Bridge Sequential Pareto Optimization for Fast Pre-Design and Final Component
Selection.” In 2024 IEEE Design Methodologies Conference (DMC), 1–8, 2024.
https://doi.org/10.1109/DMC62632.2024.10812131.
ieee: 'N. Förster, O. Wallscheid, and F. Schafmeister, “Dual-Active Bridge Sequential
Pareto Optimization for Fast Pre-Design and Final Component Selection,” in 2024
IEEE Design Methodologies Conference (DMC), 2024, pp. 1–8, doi: 10.1109/DMC62632.2024.10812131.'
mla: Förster, Nikolas, et al. “Dual-Active Bridge Sequential Pareto Optimization
for Fast Pre-Design and Final Component Selection.” 2024 IEEE Design Methodologies
Conference (DMC), 2024, pp. 1–8, doi:10.1109/DMC62632.2024.10812131.
short: 'N. Förster, O. Wallscheid, F. Schafmeister, in: 2024 IEEE Design Methodologies
Conference (DMC), 2024, pp. 1–8.'
date_created: 2026-01-06T08:06:24Z
date_updated: 2026-01-06T08:07:50Z
department:
- _id: '52'
doi: 10.1109/DMC62632.2024.10812131
keyword:
- MOSFET
- Thermal resistance
- Surface resistance
- Bridge circuits
- Zero voltage switching
- Pareto optimization
- Capacitance
- Numerical simulation
- Optimization
- Resistance heating
- Pareto Optimization
- Dual-Active Bridge
- ZVS
- Inductor Optimization
- Transformer Optimization
- Heat Sink Optimization
language:
- iso: eng
page: 1-8
publication: 2024 IEEE Design Methodologies Conference (DMC)
status: public
title: Dual-Active Bridge Sequential Pareto Optimization for Fast Pre-Design and Final
Component Selection
type: conference
user_id: '83383'
year: '2024'
...