Weak Convergence of an Iterative Method for Pseudomonotone Variational Inequalities and Fixed-Point Problems

L. C. Ceng (), M. Teboulle () and J. C. Yao ()
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L. C. Ceng: Shanghai Normal University
M. Teboulle: Tel Aviv University
J. C. Yao: National Sun Yat-sen University

Journal of Optimization Theory and Applications, 2010, vol. 146, issue 1, No 2, 19-31

Abstract: 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.

Keywords: Variational inequalities; Nonexpansive mappings; Extragradient methods; Approximate proximal methods; Pseudomonotone mappings; Fixed points; Weak convergence; Opial condition (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10957-010-9650-0

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