Algorithms for the Split Variational Inequality Problem

Yair Censor; Aviv Gibali; Simeon Reich

doi:10.1007/s11075-011-9490-5

Algorithms for the Split Variational Inequality Problem

Yair Censor, Aviv Gibali, Simeon Reich

Department of Mathematics

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

Abstract

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.

Original language	English
Pages (from-to)	301-323
Number of pages	23
Journal	Numerical Algorithms
Volume	59
Issue number	2
DOIs	https://doi.org/10.1007/s11075-011-9490-5
State	Published - Feb 2012

Bibliographical note

Funding Information:
Acknowledgements This work was partially supported by a United States-Israel Binational Science Foundation (BSF) Grant number 200912, by US Department of Army award number W81XWH-10-1-0170, by Israel Science Foundation (ISF) Grant number 647/07, by the Fund for the Promotion of Research at the Technion and by the Technion President’s Research Fund.

Keywords

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

ASJC Scopus subject areas

Applied Mathematics

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10.1007/s11075-011-9490-5

Cite this

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abstract = "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.",

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note = "Funding Information: Acknowledgements This work was partially supported by a United States-Israel Binational Science Foundation (BSF) Grant number 200912, by US Department of Army award number W81XWH-10-1-0170, by Israel Science Foundation (ISF) Grant number 647/07, by the Fund for the Promotion of Research at the Technion and by the Technion President{\textquoteright}s Research Fund.",

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KW - Inverse strongly monotone operator

KW - Iterative method

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KW - Monotone operator

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KW - Split variational inequality problem

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Algorithms for the Split Variational Inequality Problem

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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