A VERSION OF THE MIRROR DESCENT METHOD TO SOLVE VARIATIONAL INEQUALITIES*

摘要

Nemirovski and Yudin proposed the mirror descent algorithm at the late 1970s to solve convex optimization problems. This method is suitable to solve huge-scale optimization problems. In the paper, we describe a new version of the mirror descent method to solve variational inequalities with pseudomonotone operators. The method can be interpreted as a modification of Popov's two-step algorithm with the use of Bregman projections on the feasible set. We prove the convergence of the sequences generated by the proposed method.