A Second Order Dynamical System and Its Discretization for Strongly Pseudo-monotone Variational Inequalities

Abstract

We consider a second order dynamical system for solving variational inequalities in Hilbert spaces. Under standard conditions, we prove the existence and uniqueness of strong global solution of the proposed dynamical system. The exponential convergence of trajectories is established under strong pseudo-monotonicity and Lipschitz continuity assumptions. A discrete version of the proposed dynamical system leads to a relaxed inertial projection algorithm whose linear convergence is proved under suitable conditions on parameters. We discuss the possibility of extension to general monotone inclusion problems. Finally some numerical experiments are reported demonstrating the theoretical results.