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.
Bibliographical noteFunding Information:
Acknowledgements This work was partially supported by a United States-Israel Binational Science Foundation (BSF) Grant number 200912, by US Department of Army award number W81XWH-10-1-0170, by Israel Science Foundation (ISF) Grant number 647/07, by the Fund for the Promotion of Research at the Technion and by the Technion President’s Research Fund.
- Constrained variational inequality problem
- Hilbert space
- Inverse strongly monotone operator
- Iterative method
- Metric projection
- Monotone operator
- Product space
- Split inverse problem
- Split variational inequality problem
- Variational inequality problem
ASJC Scopus subject areas
- Applied Mathematics