A Douglas-Rachford splitting method for solving equilibrium problems

被引：17
作者：
Briceno-Arias, Luis M.
机构：
[1] Center for Mathematical Modeling-University of Chile, Universidad Tecnica Federico Santa María
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 16期
关键词：
Douglas-Rachford splitting; Equilibrium problem; Maximally monotone operator; Monotone inclusion; MAXIMAL MONOTONE-OPERATORS; PROXIMAL POINT ALGORITHM; REFLEXIVE BANACH-SPACES; VARIATIONAL-INEQUALITIES; CONVERGENCE; MAPPINGS;
D O I：
10.1016/j.na.2012.06.014
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We propose a splitting method for solving equilibrium problems involving the sum of two bifunctions satisfying standard conditions. We prove that this problem is equivalent to find a zero of the sum of two appropriate maximally monotone operators under a suitable qualification condition. Our algorithm is a consequence of the Douglas-Rachford splitting applied to this auxiliary monotone inclusion. Connections between monotone inclusions and equilibrium problems are studied. (C) 2012 Elsevier Ltd. All rights reserved.
引用
收藏
页码：6053 / 6059
页数：7
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