Algorithms for the Split Variational Inequality Problem

Algorithms for the Split Variational Inequality Problem

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Article ID: iaor2012266
Volume: 59
Issue: 2
Start Page Number: 301
End Page Number: 323
Publication Date: Feb 2012
Journal: Numerical Algorithms
Authors: , ,
Keywords: calculus of variations
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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