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Iterative Methods for Pseudomonotone Variational Inequalities and Fixed-Point Problems

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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.

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Acknowledgements

Y. Yao was supported in part by Colleges and Universities Science and Technology Development Foundation (20091003) of Tianjin, NSFC 11071279 and NSFC 71161001-G0105. The authors are grateful to the referees for their criticisms, comments, and suggestions which improved and strengthened the presentation of this manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, China

    Yonghong Yao

  2. Faculty of Applied Sciences, University “Politehnica” of Bucharest, Splaiul Independentei 313, Bucharest, 060042, Romania

    Mihai Postolache

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  1. Yonghong Yao
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  2. Mihai Postolache
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Correspondence to Mihai Postolache.

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Communicated by Alfredo Iusem.

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Yao, Y., Postolache, M. Iterative Methods for Pseudomonotone Variational Inequalities and Fixed-Point Problems. J Optim Theory Appl 155, 273–287 (2012). https://doi.org/10.1007/s10957-012-0055-0

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  • DOI: https://doi.org/10.1007/s10957-012-0055-0

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