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

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  • Haiyun Zhou

    (Shijiazhuang Mechanical Engineering College)

  • Peiyuan Wang

    (Shijiazhuang Mechanical Engineering College)

Abstract

In the present paper, we propose a simpler explicit iterative algorithm for finding a solution for variational inequalities over the set of common fixed points of a finite family of nonexpansive mappings on Hilbert spaces. A strong convergence theorem is proved under fewer restrictions imposed on the mappings and parameters. An extension and numerical result are also given to illustrate the effectiveness and superiority of the proposed algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:3:d:10.1007_s10957-013-0470-x
    DOI: 10.1007/s10957-013-0470-x
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    References listed on IDEAS

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    1. 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.
    2. Hong-Kun Xu, 2011. "Averaged Mappings and the Gradient-Projection Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 360-378, August.
    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.
    4. 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.
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    Cited by:

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    2. Jeong, Jae Ug, 2016. "Generalized viscosity approximation methods for mixed equilibrium problems and fixed point problems," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 168-180.

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