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Self-Adaptive Method and Inertial Modification for Solving the Split Feasibility Problem and Fixed-Point Problem of Quasi-Nonexpansive Mapping

Author

Listed:
  • Yuanheng Wang

    (College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China)

  • Tiantian Xu

    (College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China)

  • Jen-Chih Yao

    (College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China)

  • Bingnan Jiang

    (College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China)

Abstract

The split feasibility problem (SFP) has many practical applications, which has attracted the attention of many authors. In this paper, we propose a different method to solve the SFP and the fixed-point problem involving quasi-nonexpansive mappings. We relax the conditions of the operator as well as consider the inertial iteration and the adaptive step size. For example, the convergence generated by our new method is better than that of other algorithms, and the convergence rate of our algorithm greatly improves that of previous algorithms.

Suggested Citation

  • Yuanheng Wang & Tiantian Xu & Jen-Chih Yao & Bingnan Jiang, 2022. "Self-Adaptive Method and Inertial Modification for Solving the Split Feasibility Problem and Fixed-Point Problem of Quasi-Nonexpansive Mapping," Mathematics, MDPI, vol. 10(9), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1612-:d:811508
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    References listed on IDEAS

    as
    1. Rapeepan Kraikaew & Satit Saejung, 2014. "Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 399-412, November.
    2. Bingnan Jiang & Yuanheng Wang & Jen-Chih Yao, 2021. "Multi-Step Inertial Regularized Methods for Hierarchical Variational Inequality Problems Involving Generalized Lipschitzian Mappings," Mathematics, MDPI, vol. 9(17), pages 1-20, August.
    3. 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.
    4. Songnian He & Caiping Yang, 2013. "Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, May.
    5. Qiao-Li Dong & Songnian He & Michael Th. Rassias, 2021. "General splitting methods with linearization for the split feasibility problem," Journal of Global Optimization, Springer, vol. 79(4), pages 813-836, April.
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