Algorithms for the Split Variational Inequality Problem

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 l...

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Bibliographic Details
Published in:Numerical algorithms Vol. 59; no. 2; pp. 301 - 323
Main Authors: Censor, Yair, Gibali, Aviv, Reich, Simeon
Format: Journal Article
Language:English
Published: Boston Springer US 01.02.2012
Springer Nature B.V
Subjects:
Algebra
Algorithms
Computer Science
Euclidean geometry
Hilbert space
Inverse problems
Iterative algorithms
Linear transformations
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
Metric projection
Split inverse problem
Inverse strongly monotone operator
Variational inequality problem
Iterative method
Hilbert space
Monotone operator
Product space
Constrained variational inequality problem
Split variational inequality problem
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary: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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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-011-9490-5