VA & OPT Webinar: Pham Ky Anh

Title: Regularized dynamical systems associated with structured monotone inclusions

Speaker: Pham Ky Anh (Vietnam National University)

Date and Time: Wed Mar 30 2022, 17:00 AEST (Register here for remote connection via Zoom)

Abstract:

In this report, we consider two dynamical systems associated with additively structured monotone inclusions involving a multi-valued maximally monotone operator A and a single-valued operator B in real Hilbert spaces. We established strong convergence of the regularized forward-backward and regularized forward – backward–forward dynamics to an “optimal” solution of the original inclusion under a weak assumption on the single-valued operator B. Convergence estimates are obtained if the composite operator A + B is maximally monotone and strongly (pseudo)monotone. Time-discretization of the corresponding continuous dynamics provides an iterative regularization forward-backward method or an iterative regularization forward-backward-forward method with relaxation parameters. Some simple numerical examples were given to illustrate the agreement between analytical and numerical results as well as the performance of the proposed algorithms.