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Iterative Methods for Pseudomonotone Variational Inequalities and Fixed-Point Problems

Author

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  • Yonghong Yao

    (Tianjin Polytechnic University)

  • Mihai Postolache

    (University “Politehnica” of Bucharest)

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.

Suggested Citation

  • Yonghong Yao & Mihai Postolache, 2012. "Iterative Methods for Pseudomonotone Variational Inequalities and Fixed-Point Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 273-287, October.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:1:d:10.1007_s10957-012-0055-0
    DOI: 10.1007/s10957-012-0055-0
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    References listed on IDEAS

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    1. L. C. Ceng & M. Teboulle & J. C. Yao, 2010. "Weak Convergence of an Iterative Method for Pseudomonotone Variational Inequalities and Fixed-Point Problems," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 19-31, July.
    2. M. Bianchi & R. Pini, 2005. "Coercivity Conditions for Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 79-92, January.
    3. Jen-Chih Yao, 1994. "Variational Inequalities with Generalized Monotone Operators," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 691-705, August.
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    Cited by:

    1. Lateef Olakunle Jolaoso & Adeolu Taiwo & Timilehin Opeyemi Alakoya & Oluwatosin Temitope Mewomo, 2020. "A Strong Convergence Theorem for Solving Pseudo-monotone Variational Inequalities Using Projection Methods," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 744-766, June.
    2. Huan Zhang & Xiaolan Liu & Yan Sun & Ju Hu, 2023. "An Alternated Inertial Projection Algorithm for Multi-Valued Variational Inequality and Fixed Point Problems," Mathematics, MDPI, vol. 11(8), pages 1-13, April.
    3. Lu-Chuan Ceng & Xiaoye Yang, 2019. "Some Mann-Type Implicit Iteration Methods for Triple Hierarchical Variational Inequalities, Systems Variational Inequalities and Fixed Point Problems," Mathematics, MDPI, vol. 7(3), pages 1-20, February.
    4. Thi Thu Van Nguyen & Jean Jacques Strodiot & Van Hien Nguyen, 2014. "Hybrid Methods for Solving Simultaneously an Equilibrium Problem and Countably Many Fixed Point Problems in a Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 809-831, March.
    5. Yonghong Yao & Mihai Postolache & Jen-Chih Yao, 2019. "An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems," Mathematics, MDPI, vol. 7(1), pages 1-15, January.

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