Convergence of Two-Stage Method with Bregman Divergence for Solving Variational Inequalities*

Abstract

A new two-stage method is proposed for the approximate solution of variational inequalities with pseudo-monotone and Lipschitz-continuous operators acting in a finite-dimensional linear normed space. This method is a modification of several well-known two-stage algorithms using the Bregman divergence instead of the Euclidean distance. Like other schemes using Bregman divergence, the proposed method can sometimes efficiently take into account the structure of the feasible set of the problem. A theorem on the convergence of the method is proved and, in the case of a monotone operator and convex compact feasible set, non-asymptotic estimates of the efficiency of the method are obtained.