Iterative Methods for Pseudomonotone Variational Inequalities and Fixed-Point Problems

Yonghong Yao () and Mihai Postolache ()
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Yonghong Yao: Tianjin Polytechnic University
Mihai Postolache: University “Politehnica” of Bucharest

Journal of Optimization Theory and Applications, 2012, vol. 155, issue 1, No 15, 273-287

Abstract: Abstract In this paper, we introduce an iterative scheme for finding a common element of the set of solution of a pseudomonotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The proposed iterative method combines two well-known schemes: extragradient and approximate proximal methods. We derive some necessary and sufficient conditions for strong convergence of the sequences generated by the proposed scheme.

Keywords: Variational inequalities; Pseudomonotone mapping; Nonexpansive mapping; Extragradient method; Fixed point (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10957-012-0055-0

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