A von Neumann alternating method for finding common solutions to variational inequalities

Yair Censor; Aviv Gibali; Simeon Reich

doi:10.1016/j.na.2012.01.021

A von Neumann alternating method for finding common solutions to variational inequalities

Yair Censor, Aviv Gibali, Simeon Reich

Department of Mathematics

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

Abstract

By modifying von Neumann's alternating projections algorithm, we obtain an alternating method for solving the recently introduced Common Solutions to Variational Inequalities Problem (CSVIP). For simplicity, we mainly confine our attention to the two-set CSVIP, which entails finding common solutions to two unrelated variational inequalities in Hilbert space.

Original language	English
Pages (from-to)	4596-4603
Number of pages	8
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	75
Issue number	12
DOIs	https://doi.org/10.1016/j.na.2012.01.021
State	Published - Aug 2012

Bibliographical note

Funding Information:
We gratefully acknowledge a referee’s constructive comments that helped us to improve the paper. This work was partially supported by United States–Israel Binational Science Foundation (BSF) Grant number 200912 , US Department of Army Award number W81XWH-10-1-0170, Israel Science Foundation (ISF) Grant number 647/07 , the Fund for the Promotion of Research at the Technion and by the Technion VPR Fund .

Keywords

Alternating method
Averaged operator
Fixed point
Hilbert space
Inverse strongly monotone operator
Metric projection
Nonexpansive operator
Resolvent
Variational inequality

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2012.01.021

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title = "A von Neumann alternating method for finding common solutions to variational inequalities",

abstract = "By modifying von Neumann's alternating projections algorithm, we obtain an alternating method for solving the recently introduced Common Solutions to Variational Inequalities Problem (CSVIP). For simplicity, we mainly confine our attention to the two-set CSVIP, which entails finding common solutions to two unrelated variational inequalities in Hilbert space.",

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

note = "Funding Information: We gratefully acknowledge a referee{\textquoteright}s constructive comments that helped us to improve the paper. This work was partially supported by United States–Israel Binational Science Foundation (BSF) Grant number 200912 , US Department of Army Award number W81XWH-10-1-0170, Israel Science Foundation (ISF) Grant number 647/07 , the Fund for the Promotion of Research at the Technion and by the Technion VPR Fund . ",

year = "2012",

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AU - Censor, Yair

AU - Gibali, Aviv

AU - Reich, Simeon

N1 - Funding Information: We gratefully acknowledge a referee’s constructive comments that helped us to improve the paper. This work was partially supported by United States–Israel Binational Science Foundation (BSF) Grant number 200912 , US Department of Army Award number W81XWH-10-1-0170, Israel Science Foundation (ISF) Grant number 647/07 , the Fund for the Promotion of Research at the Technion and by the Technion VPR Fund .

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N2 - By modifying von Neumann's alternating projections algorithm, we obtain an alternating method for solving the recently introduced Common Solutions to Variational Inequalities Problem (CSVIP). For simplicity, we mainly confine our attention to the two-set CSVIP, which entails finding common solutions to two unrelated variational inequalities in Hilbert space.

AB - By modifying von Neumann's alternating projections algorithm, we obtain an alternating method for solving the recently introduced Common Solutions to Variational Inequalities Problem (CSVIP). For simplicity, we mainly confine our attention to the two-set CSVIP, which entails finding common solutions to two unrelated variational inequalities in Hilbert space.

KW - Alternating method

KW - Averaged operator

KW - Fixed point

KW - Hilbert space

KW - Inverse strongly monotone operator

KW - Metric projection

KW - Nonexpansive operator

KW - Resolvent

KW - Variational inequality

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M3 - Article

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VL - 75

SP - 4596

EP - 4603

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 12

ER -

A von Neumann alternating method for finding common solutions to variational inequalities

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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