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


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

All Science Journal Classification (ASJC) codes

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


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