Tikhonov regularization of a second order dynamical system with Hessian driven damping

TL;DR

This paper studies a second-order dynamical system with Hessian-driven damping and Tikhonov regularization, showing fast convergence of function values and strong convergence of trajectories to the minimum norm solution in convex optimization.

Contribution

It introduces a novel analysis of a Hessian-driven damping system with Tikhonov regularization, establishing convergence rates and strong convergence results.

Findings

Fast convergence of function values along trajectories

Strong convergence to the minimum norm minimizer

Effective use of Tikhonov regularization in dynamical systems

Abstract

We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in Hilbert spaces. We obtain fast convergence results for the function values along the trajectories. The Tikhonov regularization term enables the derivation of strong convergence results of the trajectory to the minimizer of the objective function of minimum norm.