학술논문
Convergence of a two-step method with Bregman divergence for variational inequalities.
Document Type
Journal Translation
Author
Nomirovskiĭ, D. A. (UKR-KIEV-NDM) AMS Author Profile; Rublev, B. V. (UKR-KIEV-NDM) AMS Author Profile; Semënov, V. V. (UKR-KIEV-NDM) AMS Author Profile
Source
Subject
49 Calculus of variations and optimal control; optimization -- 49J Existence theories
49J40Variational methods including variational inequalities
90Operations research, mathematical programming -- 90C Mathematical programming
90C33Complementarity and equilibrium problems and variational inequalities
49J40
90
90C33
Language
Russian
Abstract
Summary: ``A new two-step method for the approximate solution of variational inequalities with pseudo-monotone and Lipschitz-continuous operators acting in a finite@-dimensional linear normed space is proposed. This method is a modification of several previously studied two-stage algorithms using the Bregman divergence instead of the Euclidean distance. Like other schemes using Bregman divergence, the proposed method can sometimes efficiently take into account the structure of the feasible set of the problem. A theorem on the convergence of the method is proved and, in the case of a monotone operator and convex compact feasible set, non-asymptotic estimates of the efficiency of the method are obtained.''