Algorithms for the Split Variational Inequality Problem

被引：597

作者：

Censor, Yair ^{[1
]}

Gibali, Aviv ^{[2
]}

Reich, Simeon ^{[2
]}

机构：

[1] Univ Haifa, Dept Math, IL-31905 Haifa, Israel

[2] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

来源：

NUMERICAL ALGORITHMS | 2012年 / 59卷 / 02期

基金：

以色列科学基金会;

关键词：

Constrained variational inequality problem; Hilbert space; Inverse strongly monotone operator; Iterative method; Metric projection; Monotone operator; Product space; Split inverse problem; Split variational inequality problem; Variational inequality problem; WEAK-CONVERGENCE; NONEXPANSIVE-MAPPINGS; EXTRAGRADIENT METHOD; FEASIBILITY PROBLEM; CQ ALGORITHM; CONVEX-SETS; PROJECTION; OPERATORS; THEOREMS;

D O I：

10.1007/s11075-011-9490-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a prototypical Split Inverse Problem (SIP) and a new variational problem, called the Split Variational Inequality Problem (SVIP), which is a SIP. It entails finding a solution of one inverse problem (e.g., a Variational Inequality Problem (VIP)), the image of which under a given bounded linear transformation is a solution of another inverse problem such as a VIP. We construct iterative algorithms that solve such problems, under reasonable conditions, in Hilbert space and then discuss special cases, some of which are new even in Euclidean space.

引用

页码：301 / 323

页数：23

共 49 条

[1]

[Anonymous], 1997, Parallel Optimization: Theory, Algorithms, and Applications

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