%0 Journal Article
%A Semenov, Vladimir V.
%D 2018
%I Begell House
%K extragradient method, Bregman divergence, Lipschitz-continuous operator, subgradient algorithm
%N 8
%P 26-37
%R 10.1615/JAutomatInfScien.v50.i8.30
%T Modified Extragradient Method with Bregman Divergence for Variational Inequalities
%U http://dl.begellhouse.com/journals/2b6239406278e43e,2ec3cf2b062398ac,68b6f65b1a541f86.html
%V 50
%X A new method of extragradient type for the approximate solution of variational inequalities with pseudomonotone and Lipschitz-continuous operators acting in a finite-dimensional linear normed space is proposed. This method is a modification of the subgradient extragradient algorithm using Bregman divergence instead of Euclidean distance. Like other schemes using Bregman divergence the proposed method can sometimes effectively take into account a structure of a feasible set of the problem. The theorem on the method convergence is proved and in the case of a monotone operator nonasymptotic estimates of the method effectiveness are obtained
%8 2018-10-25