Algorithms for approximating minimization problems in Hilbert spaces

被引：8

作者：

Yao, Yonghong ^{[3
]}

Kang, Shin Min ^{[1
,2
]}

Liou, Yeong-Cheng ^{[4
]}

机构：

[1] Gyeongsang Natl Univ, Dept Math, Jinju 660701, South Korea

[2] Gyeongsang Natl Univ, RINS, Jinju 660701, South Korea

[3] Tianjin Polytech Univ, Dept Math, Tianjin 300160, Peoples R China

[4] Cheng Shiu Univ, Dept Informat Management, Kaohsiung 833, Taiwan

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2011年 / 235卷 / 12期

关键词：

Nonexpansive mapping; Monotone mapping; Fixed point; Equilibrium problem; Variational inequality; Minimization problem; FIXED-POINT PROBLEMS; MIXED EQUILIBRIUM PROBLEMS; VARIATIONAL INEQUALITY PROBLEMS; WEAK-CONVERGENCE THEOREMS; NONEXPANSIVE-MAPPINGS; MONOTONE MAPPINGS; ITERATIVE METHOD; BANACH-SPACES; OPTIMIZATION PROBLEMS; EXTRAGRADIENT METHOD;

D O I：

10.1016/j.cam.2010.10.055

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the following minimization problem min x epsilon Fix(S)boolean AND Omega mu/2 < Bx, x > + 1/2 parallel to x parallel to(2) - h(x). where B is a bounded linear operator, mu >= 0 is some constant, h is a potential function for (gamma) over barf, Fix(T) is the set of fixed points of nonexpansive mappings S and Omega is the solution set of an equilibrium problem. This paper introduces two new algorithms (one implicit and one explicit) that can be used to find the solution of the above minimization problem. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：3515 / 3526

页数：12

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