Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems

Abstract. We propose a prox-type method with efficiency estimate O(2−1) for approximating saddle points of convex-concave C1,1 functions and solutions of variational inequalities with monotone Lipschitz continuous operators. Application examples include matrix games, eigenvalue minimization and computing Lovasz capacity number of a graph and are illustrated by numerical experiments with large-scale matrix games and Lovasz capacity problems.