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Relaxed Inertial Tseng’s Type Method for Solving the Inclusion Problem with Application to Image Restoration

Author

Listed:
  • Jamilu Abubakar

    (Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand
    Department of Mathematics, Usmanu Danfodiyo University, Sokoto 840004, Nigeria)

  • Poom Kumam

    (Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand
    Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

  • Abdulkarim Hassan Ibrahim

    (Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand)

  • Anantachai Padcharoen

    (Department of Mathematics, Faculty of Science and Technology, Rambhai Barni Rajabhat University, Chanthaburi 22000, Thailand)

Abstract

The relaxed inertial Tseng-type method for solving the inclusion problem involving a maximally monotone mapping and a monotone mapping is proposed in this article. The study modifies the Tseng forward-backward forward splitting method by using both the relaxation parameter, as well as the inertial extrapolation step. The proposed method follows from time explicit discretization of a dynamical system. A weak convergence of the iterates generated by the method involving monotone operators is given. Moreover, the iterative scheme uses a variable step size, which does not depend on the Lipschitz constant of the underlying operator given by a simple updating rule. Furthermore, the proposed algorithm is modified and used to derive a scheme for solving a split feasibility problem. The proposed schemes are used in solving the image deblurring problem to illustrate the applicability of the proposed methods in comparison with the existing state-of-the-art methods.

Suggested Citation

  • Jamilu Abubakar & Poom Kumam & Abdulkarim Hassan Ibrahim & Anantachai Padcharoen, 2020. "Relaxed Inertial Tseng’s Type Method for Solving the Inclusion Problem with Application to Image Restoration," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:818-:d:359623
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    References listed on IDEAS

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    1. Boţ, Radu Ioan & Csetnek, Ernö Robert & Hendrich, Christopher, 2015. "Inertial Douglas–Rachford splitting for monotone inclusion problems," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 472-487.
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    5. M. Marques Alves & Jonathan Eckstein & Marina Geremia & Jefferson G. Melo, 2020. "Relative-error inertial-relaxed inexact versions of Douglas-Rachford and ADMM splitting algorithms," Computational Optimization and Applications, Springer, vol. 75(2), pages 389-422, March.
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    Cited by:

    1. Kamonrat Sombut & Kanokwan Sitthithakerngkiet & Areerat Arunchai & Thidaporn Seangwattana, 2023. "An Inertial Forward–Backward Splitting Method for Solving Modified Variational Inclusion Problems and Its Application," Mathematics, MDPI, vol. 11(9), pages 1-16, April.

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