Abstract. The mirror descent algorithm was proposed by Nemirovski and Yudin in the end of 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.

Keywords: variational inequality, pseudomonotonicity, Bregman distance, Kullback–Leibler distance, mirror descent method, convergence.