423. Inertial dynamics with vanishing Tikhonov regularization for multiobjective optimization
Invited abstract in session TB-2: Infinite-dimensional optimization - Part I, stream Nonsmooth and nonconvex optimization.
Tuesday, 10:30-12:30Room: B100/7011
Authors (first author is the speaker)
| 1. | Konstantin Sonntag
|
| Mathematics, Paderborn University |
Abstract
This talk focuses on recent developments in continuous-time dynamical systems for multiobjective optimization. Research in this area is motivated by the strong connection between accelerated first-order optimization methods and corresponding gradient-like dynamical systems. In practice, it has been shown that the analysis of continuous-time systems is often simpler and can later be translated into discrete-time optimization schemes.
In this talk, we introduce, within a Hilbert space setting, a second-order dynamical system with asymptotically vanishing damping and vanishing Tikhonov regularization, which addresses a multiobjective optimization problem with convex and differentiable components of the objective function. We explore the asymptotic behavior of trajectory solutions to this system, particularly focusing on the fast convergence of function values, quantified in terms of a merit function. Depending on the system's parameters, we establish 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.
Keywords
- Multi-objective optimization
- First-order optimization
Status: accepted
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