Algorithms for the Split Variational Inequality Problem

Authors:
Yair Censor;Aviv Gibali;Simeon Reich
Affiliations:
Department of Mathematics, University of Haifa, Mt. Carmel, Israel 31905;Department of Mathematics, The Technion - Israel Institute of Technology, Technion City, Israel 32000;Department of Mathematics, The Technion - Israel Institute of Technology, Technion City, Israel 32000
Venue:
Numerical Algorithms
Year:
2012

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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.