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An Explicit Iterative Algorithm for a Class of Variational Inequalities in Hilbert Spaces

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  • Nguyen Buong

    (VAST)

  • Lam Thuy Duong

    (Thai Nguyen University)

Abstract

In this paper, we introduce a new explicit iterative algorithm for finding a solution for variational inequalities over the set of common fixed points of a finite family of nonexpansive maps on Hilbert spaces. An application and a numerical result are given for illustration.

Suggested Citation

  • Nguyen Buong & Lam Thuy Duong, 2011. "An Explicit Iterative Algorithm for a Class of Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 513-524, December.
    • Handle: RePEc:spr:joptap:v:151:y:2011:i:3:d:10.1007_s10957-011-9890-7
    DOI: 10.1007/s10957-011-9890-7
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    References listed on IDEAS

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    1. L. C. Zeng & N. C. Wong & J. C. Yao, 2007. "Convergence Analysis of Modified Hybrid Steepest-Descent Methods with Variable Parameters for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 51-69, January.
    2. H. K. Xu & T. H. Kim, 2003. "Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 185-201, October.
    3. H.K. Xu, 2003. "An Iterative Approach to Quadratic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 659-678, March.
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    Cited by:

    1. Nguyen Buong & Nguyen Duong Nguyen & Nguyen Thi Quynh Anh, 2024. "An Inertial Iterative Regularization Method for a Class of Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 649-667, August.
    2. Haiyun Zhou & Peiyuan Wang, 2014. "A Simpler Explicit Iterative Algorithm for a Class of Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 716-727, June.

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