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

Radu Ioan Bot, Ernö Robert Csetnek, Szilárd Csaba László

Published 2019-11-28Version 1

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.