PROX-METHOD WITH RATE OF CONVERGENCE O(1/t) FOR VARIATIONAL INEQUALITIES WITH LIPSCHITZ CONTINUOUS MONOTONE OPERATORS AND SMOOTH CONVEX-CONCAVE SADDLE POINT PROBLEMS∗

We propose a prox-type method with efficiency estimate O( −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 the Lovasz capacity number of a graph, and these are illustrated by numerical experiments with large-scale matrix games and Lovasz capacity problems.