Common Solutions to Variational Inequalities

Yair Censor, Aviv Gibali, Simeon Reich, Shoham Sabach

Research output: Contribution to journalArticlepeer-review


We study the new variational inequality problem, called the Common Solutions to Variational Inequalities Problem (CSVIP). This problem consists of finding common solutions to a system of unrelated variational inequalities corresponding to set-valued mappings in Hilbert space. We present an iterative procedure for solving this problem and establish its strong convergence. Relations with other problems of solving systems of variational inequalities, both old and new, are discussed as well.

Original languageEnglish
Pages (from-to)229-247
Number of pages19
JournalSet-Valued and Variational Analysis
Issue number2
StatePublished - Jun 2012

Bibliographical note

Funding Information:
Acknowledgements We thank an anonymous referee and Sedi Bartz for their constructive comments. The work of Y. C. was partially supported by grant number 2009012 from the United States-Israel Binational Science Foundation (BSF) and by US Department of Army award number W81XWH-10-1-0170. The work of S. R. was partially supported by the Israel Science Foundation grant number 647/07, by the Fund for the Promotion of Research at the Technion and by the Technion President’s Research Fund.


  • Hilbert space
  • Iterative procedure
  • Maximal monotone mapping
  • Nonexpansive mapping
  • Variational inequality

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Numerical Analysis
  • Geometry and Topology
  • Applied Mathematics


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