Schemes for finding minimum-norm solutions of variational inequalities

被引：110

作者：

Yao, Yonghong ^{[2
]}

Chen, Rudong ^{[2
]}

Xu, Hong-Kun ^{[1
]}

机构：

[1] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan

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

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 72卷 / 7-8期

关键词：

Variational inequality; Nonexpansive mapping; Iterative algorithm; Implicit scheme; Explicit scheme; Fixed point; Minimum norm; ALGORITHM; ITERATION; SET;

D O I：

10.1016/j.na.2009.12.029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Consider the variational inequality (VI) of finding a point x* such that x* is an element of Fix(T) and <(I - S)x*, x - x*> >= 0, x is an element of Fix(T) (*) where T, S are nonexpansive self-mappings of a closed convex subset C of a Hilbert space, and Fix(T) is the set of fixed points of T. Assume that the solution set Omega of this VI is nonempty. This paper introduces two schemes, one implicit and one explicit, that can be used to find the minimum-norm solution of VI (*); namely, the unique solution x* to the quadratic minimization problem: x* = arg min(x is an element of Omega) parallel to x parallel to(2). (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：3447 / 3456

页数：10

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