IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i7p1036-d778466.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/7/1036/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/7/1036/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Adrian Marius Deaconu & Daniel Tudor Cotfas & Petru Adrian Cotfas, 2023. "Advanced Optimization Methods and Applications," Mathematics, MDPI, vol. 11(9), pages 1-7, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Adisak Hanjing & Suthep Suantai, 2023. "Novel Algorithms with Inertial Techniques for Solving Constrained Convex Minimization Problems and Applications to Image Inpainting," Mathematics, MDPI, vol. 11(8), pages 1-18, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1036-:d:778466. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.