Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping
K. Sonntag, S. Peitz, ArXiv:2307.00975 (2023).
Download (ext.)
Preprint
| English
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 laid out in [H.
Attouch and G. Garrigos, Multiobjective optimization: an inertial approach to
Pareto optima, preprint, arXiv:1506.02823, 201]. 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 $O(t^{-2})$ 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.
Publishing Year
Journal Title
arXiv:2307.00975
LibreCat-ID
Cite this
Sonntag K, Peitz S. Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping. arXiv:230700975. Published online 2023.
Sonntag, K., & Peitz, S. (2023). Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping. In arXiv:2307.00975.
@article{Sonntag_Peitz_2023, title={Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping}, journal={arXiv:2307.00975}, author={Sonntag, Konstantin and Peitz, Sebastian}, year={2023} }
Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping.” ArXiv:2307.00975, 2023.
K. Sonntag and S. Peitz, “Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping,” arXiv:2307.00975. 2023.
Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping.” ArXiv:2307.00975, 2023.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]
Link(s) to Main File(s)
Access Level
