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Modified Projection Method with Inertial Technique and Hybrid Stepsize for the Split Feasibility Problem

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  • Suthep Suantai

    (Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Suparat Kesornprom

    (School of Science, University of Phayao, Phayao 56000, Thailand)

  • Watcharaporn Cholamjiak

    (School of Science, University of Phayao, Phayao 56000, Thailand)

  • Prasit Cholamjiak

    (School of Science, University of Phayao, Phayao 56000, Thailand)

Abstract

We designed a modified projection method with a new condition of the inertial step and the step size for the split feasibility problem in Hilbert spaces. We show that our iterate weakly converged to a solution. Lastly, we give numerical examples and comparisons that could be applied to signal recovery to show the efficiency of our method.

Suggested Citation

  • Suthep Suantai & Suparat Kesornprom & Watcharaporn Cholamjiak & Prasit Cholamjiak, 2022. "Modified Projection Method with Inertial Technique and Hybrid Stepsize for the Split Feasibility Problem," Mathematics, MDPI, vol. 10(6), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:933-:d:771284
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    References listed on IDEAS

    as
    1. Charles L. Byrne and Abdellatif Moudafi, 2013. "Extensions of the CQ Algorithm for the Split Feasibility and Split Equality Problems," Documents de Travail 2013-01, CEREGMIA, Université des Antilles et de la Guyane.
    2. Adisak Hanjing & Suthep Suantai, 2020. "A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method," Mathematics, MDPI, vol. 8(3), pages 1-13, March.
    3. Zhao-Rong Kong & Lu-Chuan Ceng & Ching-Feng Wen, 2012. "Some Modified Extragradient Methods for Solving Split Feasibility and Fixed Point Problems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-32, December.
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    Cited by:

    1. Habib ur Rehman & Wiyada Kumam & Kamonrat Sombut, 2022. "Inertial Modification Using Self-Adaptive Subgradient Extragradient Techniques for Equilibrium Programming Applied to Variational Inequalities and Fixed-Point Problems," Mathematics, MDPI, vol. 10(10), pages 1-29, May.

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