Multistep Hybrid Extragradient Method for Triple Hierarchical Variational Inequalities

被引：6

作者：

Kong, Zhao-Rong ^{[1
]}

Ceng, Lu-Chuan ^{[2
,3
]}

Ansari, Qamrul Hasan ^{[4
]}

Pang, Chin-Tzong ^{[5
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[3] Sci Comp Key Lab Shanghai Univ, Shanghai 200234, Peoples R China

[4] Aligarh Muslim Univ, Dept Math, Aligarh 20200, Uttar Pradesh, India

[5] Yuan Ze Univ, Dept Informat Management, Chungli 32003, Taiwan

来源：

ABSTRACT AND APPLIED ANALYSIS | 2013年

基金：

美国国家科学基金会;

关键词：

FIXED-POINT APPROACH; VISCOSITY APPROXIMATION METHODS; STRONG-CONVERGENCE THEOREMS; ITERATIVE ALGORITHMS; DESCENT METHOD; SET;

D O I：

10.1155/2013/718624

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a triple hierarchical variational inequality problem (THVIP), that is, a variational inequality problem defined over the set of solutions of another variational inequality problem which is defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Moreover, we propose a multistep hybrid extragradient method to compute the approximate solutions of the THVIP and present the convergence analysis of the sequence generated by the proposed method. We also derive a solution method for solving a system of hierarchical variational inequalities (SHVI), that is, a system of variational inequalities defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Under very mild conditions, it is proven that the sequence generated by the proposed method converges strongly to a unique solution of the SHVI.

引用

页数：17

共 34 条

[1]

[Anonymous], PACIFIC J OPTIM

[2]

BERTSEKAS DP, 1982, MATH PROGRAM STUD, V17, P139

[3] A unified treatment of some iterative algorithms in signal processing and image reconstruction [J].

Byrne, C .

INVERSE PROBLEMS, 2004, 20 (01) :103-120

[4] Proximal point algorithm controlled by a slowly vanishing term: Applications to hierarchical minimization [J].

Cabot, A .

SIAM JOURNAL ON OPTIMIZATION, 2005, 15 (02) :555-572

[5]

Ceng L. C., 2012, FIXED POINT THEORY, V13, P403

[6]

Ceng L. C., ABSTRACT AP IN PRESS

[7]

Ceng LC, 2007, FIXED POINT THEOR-RO, V8, P219

[8] HYBRID METHOD FOR DESIGNING EXPLICIT HIERARCHICAL FIXED POINT APPROACH TO MONOTONE VARIATIONAL INEQUALITIES [J].

Ceng, Lu-Chuan ;

Lin, Yen-Cherng ;

Petrusel, Adrian .

TAIWANESE JOURNAL OF MATHEMATICS, 2012, 16 (04) :1531-1555

[9] Iterative Methods for Triple Hierarchical Variational Inequalities in Hilbert Spaces [J].

Ceng, Lu-Chuan ;

Ansari, Qamrul Hasan ;

Yao, Jen-Chih .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2011, 151 (03) :489-512

[10] 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

← 1 2 3 4 →