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The Modified Viscosity Approximation Method with Inertial Technique and Forward–Backward Algorithm for Convex Optimization Model

Author

Listed:
  • Adisak Hanjing

    (Department of Science and Mathematics, Rajamangala University of Technology Isan Surin Campus, Surin 32000, Thailand)

  • Limpapat Bussaban

    (Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • 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)

Abstract

In this paper, we propose a new accelerated algorithm for finding a common fixed point of nonexpansive operators, and then, a strong convergence result of the proposed method is discussed and analyzed in real Hilbert spaces. As an application, we create a new accelerated viscosity forward–backward method (AVFBM) for solving nonsmooth optimization problems of the sum of two objective functions in real Hilbert spaces, and the strong convergence of AVFBM to a minimizer of the sum of two convex functions is established. We also present the application and simulated results of AVFBM for image restoration and data classification problems.

Suggested Citation

  • Adisak Hanjing & Limpapat Bussaban & Suthep Suantai, 2022. "The Modified Viscosity Approximation Method with Inertial Technique and Forward–Backward Algorithm for Convex Optimization Model," Mathematics, MDPI, vol. 10(7), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1036-:d:778466
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    References listed on IDEAS

    as
    1. Songnian He & Jun Guo, 2012. "Iterative Algorithm for Common Fixed Points of Infinite Family of Nonexpansive Mappings in Banach Spaces," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, March.
    2. Suthep Suantai & Kunrada Kankam & Prasit Cholamjiak, 2020. "A Novel Forward-Backward Algorithm for Solving Convex Minimization Problem in Hilbert Spaces," Mathematics, MDPI, vol. 8(1), pages 1-13, January.
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    Cited by:

    1. Adrian Marius Deaconu & Daniel Tudor Cotfas & Petru Adrian Cotfas, 2023. "Advanced Optimization Methods and Applications," Mathematics, MDPI, vol. 11(9), pages 1-7, May.
    2. Dawan Chumpungam & Panitarn Sarnmeta & Suthep Suantai, 2022. "An Accelerated Convex Optimization Algorithm with Line Search and Applications in Machine Learning," Mathematics, MDPI, vol. 10(9), pages 1-20, April.

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