@article{57472,
  abstract     = {{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       = {{Bot, Radu Ioan and Sonntag, Konstantin}},
  journal      = {{Journal of Mathematical Analysis and Applications}},
  keywords     = {{Pareto optimization, Lyapunov analysis, gradient-like dynamical systems, inertial dynamics, asymptotic vanishing damping, Tikhonov regularization, strong convergence}},
  title        = {{{Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization}}},
  year         = {{2025}},
}

@article{32447,
  abstract     = {{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.}},
  author       = {{Sonntag, Konstantin and Peitz, Sebastian}},
  issn         = {{1095-7189}},
  journal      = {{SIAM Journal on Optimization}},
  keywords     = {{multiobjective optimization, Pareto optimization, Lyapunov analysis, gradient-likedynamical systems, inertial dynamics, asymptotic vanishing damping, fast convergence}},
  number       = {{3}},
  pages        = {{2259 -- 2286}},
  publisher    = {{Society for Industrial and Applied Mathematics}},
  title        = {{{Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping}}},
  doi          = {{10.1137/23M1588512}},
  volume       = {{34}},
  year         = {{2024}},
}

@inproceedings{36462,
  abstract     = {{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       = {{Stephan, Richard and Brosius, Alexander}},
  booktitle    = {{The 28th Saxon Conference on Forming Technology SFU and the 7th International Conference on Accuracy in Forming Technology ICAFT}},
  keywords     = {{clinching, mechanical joining, damping, model, evaluation, dynamics}},
  publisher    = {{MDPI}},
  title        = {{{Experimental Measurement Method and Evaluation of an Analytical Approach for Sound Conduction through Multiple Clinched Sheets}}},
  doi          = {{10.3390/engproc2022026025}},
  year         = {{2022}},
}