Weak convergence of an iterative method for pseudomonotone variational inequalities and fixed-point problems

L. C. Ceng, M. Teboulle, J. C. Yao

Research output: Contribution to journalArticlepeer-review

Abstract

We consider an iterative scheme for finding a common element of the set of solutions of a pseudomonotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of N nonexpansive mappings. The proposed iterative method combines two well-known schemes: extragradient and approximate proximal methods. We derive a necessary and sufficient condition for weak convergence of the sequences generated by the proposed scheme.

Original languageEnglish
Pages (from-to)19-31
Number of pages13
JournalJournal of Optimization Theory and Applications
Volume146
Issue number1
DOIs
StatePublished - Jul 2010

Keywords

  • Approximate proximal methods
  • Extragradient methods
  • Fixed points
  • Nonexpansive mappings
  • Opial condition
  • Pseudomonotone mappings
  • Variational inequalities
  • Weak convergence

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