CONSTRUCTION OF ITERATIVE METHODS FOR VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS

被引：5

作者：

Yao, Yonghong ^{[2
]}

Liou, Yeong-Cheng ^{[3
]}

Shahzad, Naseer ^{[1
]}

机构：

[1] King Abdulaziz Univ, Dept Math, Jeddai 21589 1, Saudi Arabia

[2] Tianjin Polytech Univ, Dept Math, Tianjin, Peoples R China

[3] Cheng Shiu Univ, Dept Informat Management, Kaohsiung, Taiwan

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2012年 / 33卷 / 10期

关键词：

Fixed point; Inverse-strongly monotone mapping; Nonexpansive mapping; Strong convergence; Variational inequality; STRONG-CONVERGENCE THEOREMS; VISCOSITY APPROXIMATION METHODS; NONEXPANSIVE-MAPPINGS; MONOTONE MAPPINGS; EXTRAGRADIENT METHOD; REGULARIZATION; OPTIMIZATION; SPACES;

D O I：

10.1080/01630563.2012.660796

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we first introduce two iterative methods for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a Hilbert space. Then we show that the proposed iterative methods converge strongly to a minimum norm element of two sets.

引用

页码：1250 / 1267

页数：18

共 28 条

[21] Convergence of hybrid steepest-descent methods for variational inequalities [J].

Xu, HK ;

Kim, TH .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2003, 119 (01) :185-201

[22] VISCOSITY METHOD FOR HIERARCHICAL FIXED POINT APPROACH TO VARIATIONAL INEQUALITIES [J].

Xu, Hong-Kun .

TAIWANESE JOURNAL OF MATHEMATICS, 2010, 14 (02) :463-478

[23] Hybrid steepest descent method for variational inequality problem over the fixed point set of certain quasi-nonexpansive mappings [J].

Yamada, I ;

Ogura, N .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2004, 25 (7-8) :619-655

[24] Two-step projection methods for a system of variational inequality problems in Banach spaces [J].

Yao, Yonghong ;

Liou, Yeong-Cheng ;

Kang, Shin Min .

JOURNAL OF GLOBAL OPTIMIZATION, 2013, 55 (04) :801-811

[25] A unified implicit algorithm for solving the triple-hierarchical constrained optimization problem [J].

Yao, Yonghong ;

Chen, Rudong ;

Liou, Yeong-Cheng .

MATHEMATICAL AND COMPUTER MODELLING, 2012, 55 (3-4) :1506-1515

[26] On modified iterative method for nonexpansive mappings and monotone mappings [J].

Yao, Yonghong ;

Yao, Jen-Chih .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 186 (02) :1551-1558

[27] Strong convergence theorems for monotone mappings and relatively weak nonexpansive mappings [J].

Zegeye, Habtu ;

Shahzad, Naseer .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (07) :2707-2716

[28]

Zeng LC, 2006, TAIWAN J MATH, V10, P1293

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