A von Neumann alternating method for finding common solutions to variational inequalities

Yair Censor, Aviv Gibali, Simeon Reich

Research output: Contribution to journalArticlepeer-review


By modifying von Neumann's alternating projections algorithm, we obtain an alternating method for solving the recently introduced Common Solutions to Variational Inequalities Problem (CSVIP). For simplicity, we mainly confine our attention to the two-set CSVIP, which entails finding common solutions to two unrelated variational inequalities in Hilbert space.

Original languageEnglish
Pages (from-to)4596-4603
Number of pages8
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number12
StatePublished - Aug 2012

Bibliographical note

Funding Information:
We gratefully acknowledge a referee’s constructive comments that helped us to improve the paper. This work was partially supported by United States–Israel Binational Science Foundation (BSF) Grant number 200912 , US Department of Army Award number W81XWH-10-1-0170, Israel Science Foundation (ISF) Grant number 647/07 , the Fund for the Promotion of Research at the Technion and by the Technion VPR Fund .


  • Alternating method
  • Averaged operator
  • Fixed point
  • Hilbert space
  • Inverse strongly monotone operator
  • Metric projection
  • Nonexpansive operator
  • Resolvent
  • Variational inequality

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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