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Hybrid Conjugate Gradient Method for a Convex Optimization Problem over the Fixed-Point Set of a Nonexpansive Mapping

Author

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  • H. Iiduka

    (Tokyo Institute of Technology)

Abstract

The main aim of the paper is to accelerate the existing method for a convex optimization problem over the fixed-point set of a nonexpansive mapping. To achieve this goal, we present an algorithm (Algorithm 3.1) by using the conjugate gradient direction. We present also a convergence analysis (Theorem 3.1) under some assumptions. Finally, to demonstrate the effectiveness and performance of the proposed method, we present numerical comparisons of the existing method with the proposed method.

Suggested Citation

  • H. Iiduka, 2009. "Hybrid Conjugate Gradient Method for a Convex Optimization Problem over the Fixed-Point Set of a Nonexpansive Mapping," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 463-475, March.
    • Handle: RePEc:spr:joptap:v:140:y:2009:i:3:d:10.1007_s10957-008-9463-6
    DOI: 10.1007/s10957-008-9463-6
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    Citations

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    Cited by:

    1. Lu-Chuan Ceng & Qamrul Hasan Ansari & Jen-Chih Yao, 2011. "Iterative Methods for Triple Hierarchical Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 489-512, December.
    2. Phan Tu Vuong & Jean Jacques Strodiot & Van Hien Nguyen, 2012. "Extragradient Methods and Linesearch Algorithms for Solving Ky Fan Inequalities and Fixed Point Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 605-627, November.
    3. Hideaki Iiduka, 2011. "Decentralized Algorithm for Centralized Variational Inequalities in Network Resource Allocation," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 525-540, December.
    4. 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.
    5. Le Quang Thuy & Trinh Ngoc Hai, 2017. "A Projected Subgradient Algorithm for Bilevel Equilibrium Problems and Applications," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 411-431, November.
    6. F. U. Ogbuisi & F. O. Isiogugu & J. M. Ngnotchouye, 2021. "Approximating a common solution of extended split equality equilibrium and fixed point problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(1), pages 46-61, March.
    7. Hideaki Iiduka, 2011. "Iterative Algorithm for Solving Triple-Hierarchical Constrained Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 580-592, March.
    8. Phan Vuong & Jean Strodiot & Van Nguyen, 2014. "Projected viscosity subgradient methods for variational inequalities with equilibrium problem constraints in Hilbert spaces," Journal of Global Optimization, Springer, vol. 59(1), pages 173-190, May.
    9. Ying Liu & Hang Kong, 2019. "Strong convergence theorems for relatively nonexpansive mappings and Lipschitz-continuous monotone mappings in Banach spaces," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(4), pages 1049-1065, December.

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