A variant of mirror descent method for solving variational inequalities

We consider a variational inequalities with Lipschitz continuous pseudo-monotone operators. Many operation research problems in applications can be stated in this form. We study new variant of mirror descent algorithm (mirror-prox algorithm) for solving the variational inequalities. This method can be interpreted as the modification of well known two-stage L. Popov method with the projection onto the feasible set in the sense of Bregman divergence. Our method, like other mirror descent schemes, can effectively take into account the structure of the feasible set of the problem. The main result is the proof of the theorem about the convergence of the algorithm.