Bregman Extragradient Method with Monotone Rule of Step Adjustment*

A new extragradient-type method is proposed for approximate solution of variational inequalities with pseudo-monotone and Lipschitz-continuous operators acting in a finite-dimensional linear normed space. The method uses Bregman divergence (distance) instead of Euclidean distance and a new adjustment of step size, which does not require knowledge of the Lipschitz constant of the operator. In contrast to the previously used rules for choosing the step size, the method proposed in the paper does not perform additional calculations for the operator values and prox-map. A theorem on the convergence of the method is proved.