Algorithms for the Split Variational Inequality Problem

Details Algorithms for the Split Variational Inequality Problem Algorithms for the Split Variational Inequality Problem

2010-09-20

arxiv.org/abs/1009.3780v2

Mathematics

Optimization and Control

This is a revised version of arXiv:1009.3780v1. Accepted for publication in the journal Numerical Algorithms

Scientific paper

10.1007/s11075-011-9490-5

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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