---
_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. <i>Journal of Mathematical Analysis and Applications</i>.
    Published online 2025.
  apa: Bot, R. I., &#38; Sonntag, K. (2025). Inertial dynamics with vanishing Tikhonov
    regularization for multobjective optimization. <i>Journal of Mathematical Analysis
    and Applications</i>.
  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.” <i>Journal of Mathematical
    Analysis and Applications</i>, 2025.
  ieee: R. I. Bot and K. Sonntag, “Inertial dynamics with vanishing Tikhonov regularization
    for multobjective optimization,” <i>Journal of Mathematical Analysis and Applications</i>,
    2025.
  mla: Bot, Radu Ioan, and Konstantin Sonntag. “Inertial Dynamics with Vanishing Tikhonov
    Regularization for Multobjective Optimization.” <i>Journal of Mathematical Analysis
    and Applications</i>, 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. <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: '36462'
abstract:
- lang: eng
  text: The conduction of structure-borne sound through joints causes energy dissipation.
    The sound reduction index describes this energy loss as a level decrease in the
    particle velocity across series-connected damping elements for which the superposition
    principle applies. This simple model can help to develop a testing method for
    joints based on this characteristic energy loss. In this paper, this model is
    experimentally evaluated for multiple in-series clinched aluminium sheets. Samples
    connected by several clinch points arranged in parallel are investigated experimentally,
    and the results are discussed.
author:
- first_name: Richard
  full_name: Stephan, Richard
  last_name: Stephan
- first_name: Alexander
  full_name: Brosius, Alexander
  last_name: Brosius
citation:
  ama: 'Stephan R, Brosius A. Experimental Measurement Method and Evaluation of an
    Analytical Approach for Sound Conduction through Multiple Clinched Sheets. In:
    <i>The 28th Saxon Conference on Forming Technology SFU and the 7th International
    Conference on Accuracy in Forming Technology ICAFT</i>. MDPI; 2022. doi:<a href="https://doi.org/10.3390/engproc2022026025">10.3390/engproc2022026025</a>'
  apa: Stephan, R., &#38; Brosius, A. (2022). Experimental Measurement Method and
    Evaluation of an Analytical Approach for Sound Conduction through Multiple Clinched
    Sheets. <i>The 28th Saxon Conference on Forming Technology SFU and the 7th International
    Conference on Accuracy in Forming Technology ICAFT</i>. <a href="https://doi.org/10.3390/engproc2022026025">https://doi.org/10.3390/engproc2022026025</a>
  bibtex: '@inproceedings{Stephan_Brosius_2022, title={Experimental Measurement Method
    and Evaluation of an Analytical Approach for Sound Conduction through Multiple
    Clinched Sheets}, DOI={<a href="https://doi.org/10.3390/engproc2022026025">10.3390/engproc2022026025</a>},
    booktitle={The 28th Saxon Conference on Forming Technology SFU and the 7th International
    Conference on Accuracy in Forming Technology ICAFT}, publisher={MDPI}, author={Stephan,
    Richard and Brosius, Alexander}, year={2022} }'
  chicago: Stephan, Richard, and Alexander Brosius. “Experimental Measurement Method
    and Evaluation of an Analytical Approach for Sound Conduction through Multiple
    Clinched Sheets.” In <i>The 28th Saxon Conference on Forming Technology SFU and
    the 7th International Conference on Accuracy in Forming Technology ICAFT</i>.
    MDPI, 2022. <a href="https://doi.org/10.3390/engproc2022026025">https://doi.org/10.3390/engproc2022026025</a>.
  ieee: 'R. Stephan and A. Brosius, “Experimental Measurement Method and Evaluation
    of an Analytical Approach for Sound Conduction through Multiple Clinched Sheets,”
    2022, doi: <a href="https://doi.org/10.3390/engproc2022026025">10.3390/engproc2022026025</a>.'
  mla: Stephan, Richard, and Alexander Brosius. “Experimental Measurement Method and
    Evaluation of an Analytical Approach for Sound Conduction through Multiple Clinched
    Sheets.” <i>The 28th Saxon Conference on Forming Technology SFU and the 7th International
    Conference on Accuracy in Forming Technology ICAFT</i>, MDPI, 2022, doi:<a href="https://doi.org/10.3390/engproc2022026025">10.3390/engproc2022026025</a>.
  short: 'R. Stephan, A. Brosius, in: The 28th Saxon Conference on Forming Technology
    SFU and the 7th International Conference on Accuracy in Forming Technology ICAFT,
    MDPI, 2022.'
date_created: 2023-01-12T13:55:07Z
date_updated: 2023-01-12T13:58:49Z
department:
- _id: '630'
doi: 10.3390/engproc2022026025
keyword:
- clinching
- mechanical joining
- damping
- model
- evaluation
- dynamics
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://www.mdpi.com/2673-4591/26/1/25
oa: '1'
project:
- _id: '130'
  grant_number: '418701707'
  name: 'TRR 285: TRR 285'
- _id: '133'
  name: 'TRR 285 - C: TRR 285 - Project Area C'
- _id: '148'
  name: 'TRR 285 – C04: TRR 285 - Subproject C04'
publication: The 28th Saxon Conference on Forming Technology SFU and the 7th International
  Conference on Accuracy in Forming Technology ICAFT
publication_status: published
publisher: MDPI
status: public
title: Experimental Measurement Method and Evaluation of an Analytical Approach for
  Sound Conduction through Multiple Clinched Sheets
type: conference
user_id: '7850'
year: '2022'
...