---
_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'
...