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

Funding

FundersFunder number
Leading Academic Discipline Project of Shanghai Normal UniversityDZL707
National Natural Science Foundation of China10771141
Ministry of Education of the People's Republic of China20070270004
Shanghai Municipal Education Commission09ZZ133
Science and Technology Commission of Shanghai Municipality075105118
Shanghai Leading Academic Discipline ProjectNSC 98-2923-E-110-003-MY3, S30405

    Keywords

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

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