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
ISSN
1019-5262 (print)
Abstract
Summary: ``A new two-step method for the approximate solution ofvariational inequalities with pseudo-monotone and Lipschitz-continuousoperators acting in a finite@-dimensional linear normed space isproposed. This method is a modification of several previously studiedtwo-stage algorithms using the Bregman divergence instead of theEuclidean distance. Like other schemes using Bregman divergence, theproposed method can sometimes efficiently take into account thestructure of the feasible set of the problem. A theorem on theconvergence of the method is proved and, in the case of a monotoneoperator and convex compact feasible set, non-asymptotic estimates ofthe efficiency of the method are obtained.''