Article ID: | iaor2012266 |
Volume: | 59 |
Issue: | 2 |
Start Page Number: | 301 |
End Page Number: | 323 |
Publication Date: | Feb 2012 |
Journal: | Numerical Algorithms |
Authors: | Censor Yair, Reich Simeon, Gibali Aviv |
Keywords: | calculus of variations |
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.