Common Solutions to Variational Inequalities

Yair Censor; Aviv Gibali; Simeon Reich; Shoham Sabach

doi:10.1007/s11228-011-0192-x

Common Solutions to Variational Inequalities

Yair Censor, Aviv Gibali, Simeon Reich, Shoham Sabach

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the new variational inequality problem, called the Common Solutions to Variational Inequalities Problem (CSVIP). This problem consists of finding common solutions to a system of unrelated variational inequalities corresponding to set-valued mappings in Hilbert space. We present an iterative procedure for solving this problem and establish its strong convergence. Relations with other problems of solving systems of variational inequalities, both old and new, are discussed as well.

Original language	English
Pages (from-to)	229-247
Number of pages	19
Journal	Set-Valued and Variational Analysis
Volume	20
Issue number	2
DOIs	https://doi.org/10.1007/s11228-011-0192-x
State	Published - Jun 2012

Bibliographical note

Funding Information:
Acknowledgements We thank an anonymous referee and Sedi Bartz for their constructive comments. The work of Y. C. was partially supported by grant number 2009012 from the United States-Israel Binational Science Foundation (BSF) and by US Department of Army award number W81XWH-10-1-0170. The work of S. R. was partially supported by the Israel Science Foundation grant number 647/07, by the Fund for the Promotion of Research at the Technion and by the Technion President’s Research Fund.

Keywords

Hilbert space
Iterative procedure
Maximal monotone mapping
Nonexpansive mapping
Variational inequality

ASJC Scopus subject areas

Analysis
Statistics and Probability
Numerical Analysis
Geometry and Topology
Applied Mathematics

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10.1007/s11228-011-0192-x

Cite this

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title = "Common Solutions to Variational Inequalities",

abstract = "We study the new variational inequality problem, called the Common Solutions to Variational Inequalities Problem (CSVIP). This problem consists of finding common solutions to a system of unrelated variational inequalities corresponding to set-valued mappings in Hilbert space. We present an iterative procedure for solving this problem and establish its strong convergence. Relations with other problems of solving systems of variational inequalities, both old and new, are discussed as well.",

keywords = "Hilbert space, Iterative procedure, Maximal monotone mapping, Nonexpansive mapping, Variational inequality",

author = "Yair Censor and Aviv Gibali and Simeon Reich and Shoham Sabach",

note = "Funding Information: Acknowledgements We thank an anonymous referee and Sedi Bartz for their constructive comments. The work of Y. C. was partially supported by grant number 2009012 from the United States-Israel Binational Science Foundation (BSF) and by US Department of Army award number W81XWH-10-1-0170. The work of S. R. was partially supported by the Israel Science Foundation grant number 647/07, by the Fund for the Promotion of Research at the Technion and by the Technion President{\textquoteright}s Research Fund.",

year = "2012",

month = jun,

doi = "10.1007/s11228-011-0192-x",

language = "English",

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N2 - We study the new variational inequality problem, called the Common Solutions to Variational Inequalities Problem (CSVIP). This problem consists of finding common solutions to a system of unrelated variational inequalities corresponding to set-valued mappings in Hilbert space. We present an iterative procedure for solving this problem and establish its strong convergence. Relations with other problems of solving systems of variational inequalities, both old and new, are discussed as well.

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KW - Maximal monotone mapping

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Common Solutions to Variational Inequalities

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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