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Hybrid Proximal Point Algorithm and Applications to Equilibrium Problems and Convex Programming

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  • Vahid Dadashi

    (Islamic Azad University)

  • Mihai Postolache

    (China Medical University
    University Politehnica of Bucharest)

Abstract

In this paper, a hybrid projection algorithm for a countable family of mappings is considered in Banach spaces. The sequence generated by algorithm converges strongly to the common fixed point of the mappings. We apply the result for the resolvent of a maximal monotone operator for finding a zero of it, which is a solution of the equilibrium problem. The results obtained extend the research in this context, such as the corresponding results of Aoyama et al. (Nonlinear Anal 71(12):1626–1632, 2009, nonlinear analysis and optimization, Yokohama Publishers, Yokohama, pp. 1–17, 2009), Solodov et al. (Math Program 87(1):189–202, 2000), Ohsawa et al. (Arch Math 81(4):439–445, 2003) and Kamimura et al. (SIAM J Optim 13(3):938–945, 2002).

Suggested Citation

  • Vahid Dadashi & Mihai Postolache, 2017. "Hybrid Proximal Point Algorithm and Applications to Equilibrium Problems and Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 518-529, August.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:2:d:10.1007_s10957-017-1117-0
    DOI: 10.1007/s10957-017-1117-0
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    References listed on IDEAS

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    1. B. Djafari Rouhani & H. Khatibzadeh, 2008. "On the Proximal Point Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 411-417, May.
    2. Hadi Khatibzadeh & Sajad Ranjbar, 2013. "On the Strong Convergence of Halpern Type Proximal Point Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 385-396, August.
    3. Hadi Khatibzadeh, 2012. "Some Remarks on the Proximal Point Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 769-778, June.
    4. L. Li & W. Song, 2008. "Modified Proximal-Point Algorithm for Maximal Monotone Operators in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 45-64, July.
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    Cited by:

    1. Annel Thembinkosi Bokodisa & Lateef Olakunle Jolaoso & Maggie Aphane, 2021. "Halpern-Subgradient Extragradient Method for Solving Equilibrium and Common Fixed Point Problems in Reflexive Banach Spaces," Mathematics, MDPI, vol. 9(7), pages 1-24, March.

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