HIERARCHICAL VARIATIONAL INCLUSION PROBLEMS IN HILBERT SPACES WITH APPLICATIONS

被引：0

作者：

Chang, Shih-sen ^{[1
]}

Cho, Yeol Je ^{[2
,3
]}

Kim, Jong Kyu ^{[4
]}

机构：

[1] Yunnan Univ Finance & Econ, Coll Stat & Math, Kunming 650221, Yunnan, Peoples R China

[2] Gyeongsang Natl Univ, Dept Math Educ, Chinju 660701, South Korea

[3] Gyeongsang Natl Univ, RINS, Chinju 660701, South Korea

[4] Kyungnam Univ, Dept Math Educ, Masan 631701, South Korea

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2012年 / 13卷 / 03期

基金：

新加坡国家研究基金会;

关键词：

Hierarchical variational inclusion; quadratic minimization problem; convex programming problem; variational inclusion; multi-valued maximal monotone mapping; inverse-strongly monotone mapping; rsolvent operator; FIXED-POINT APPROACH; VISCOSITY METHOD; INEQUALITIES;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is, by using the implicit extra-gradient method, to study the existence and approximation problems of solutions of hierarchical variational inclusion problems in Hilbert spaces. Under suitable conditions, it is shown that the net defined by the suggested implicit extra-gradient method converges strongly to the unique solution of the hierarchical variational inclusion. As applications, we utilize the main results to study the quadratic minimization problems and convex programming problems.

引用

页码：503 / 513

页数：11

共 22 条

[1]

[Anonymous], 1978, Nonlinear mappings of monotone type

[2]

[Anonymous], J APPL MATH

[3]

Chang S S., 2002, Iterative methods for nonlinear operator equations in Banach spaces

[4] Set-valued variational inclusions in Banach spaces [J].

Chang, SS .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 248 (02) :438-454

[5]

Chang SS, 2001, NONLINEAR ANAL-THEOR, V47, P583

[6] On a Two-Step Algorithm for Hierarchical Fixed Point Problems and Variational Inequalities [J].

Cianciaruso, Filomena ;

Marino, Giuseppe ;

Muglia, Luigi ;

Yao, Yonghong .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2009,

[7] ON AN IMPLICIT HIERARCHICAL FIXED POINT APPROACH TO VARIATIONAL INEQUALITIES [J].

Cianciaruso, Filomena ;

Colao, Vittorio ;

Muglia, Luigi ;

Xu, Hong-Kun .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2009, 80 (01) :117-124

[8]

Demyanov V. F., 1996, Quasidifferentiability and Nonsmooth Modeling in Mechanics, Engineering and Economics

[9]

Mainge PE., 2007, PACIFIC J OPTIM, V3, P529

[10] The split common fixed-point problem for demicontractive mappings [J].

Moudafi, A. .

INVERSE PROBLEMS, 2010, 26 (05)

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