Algorithms for the Split Variational Inequality Problem

Yair Censor, Aviv Gibali, Simeon Reich

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)301-323
Number of pages23
JournalNumerical Algorithms
Issue number2
StatePublished - Feb 2012

Bibliographical note

Funding 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


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