IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i6p874-d767601.html
   My bibliography  Save this article

An Inertial Extragradient Direction Method with Self-Adaptive Step Size for Solving Split Minimization Problems and Its Applications to Compressed Sensing

Author

Listed:
  • Nattakarn Kaewyong

    (Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand)

  • Kanokwan Sitthithakerngkiet

    (Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand)

Abstract

The purpose of this work is to construct iterative methods for solving a split minimization problem using a self-adaptive step size, conjugate gradient direction, and inertia technique. We introduce and prove a strong convergence theorem in the framework of Hilbert spaces. We then demonstrate numerically how the extrapolation factor ( θ n ) in the inertia term and a step size parameter affect the performance of our proposed algorithm. Additionally, we apply our proposed algorithms to solve the signal recovery problem. Finally, we compared our algorithm’s recovery signal quality performance to that of three previously published works.

Suggested Citation

  • Nattakarn Kaewyong & Kanokwan Sitthithakerngkiet, 2022. "An Inertial Extragradient Direction Method with Self-Adaptive Step Size for Solving Split Minimization Problems and Its Applications to Compressed Sensing," Mathematics, MDPI, vol. 10(6), pages 1-25, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:874-:d:767601
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/6/874/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/6/874/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Boikanyo, Oganeditse A., 2015. "A strongly convergent algorithm for the split common fixed point problem," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 844-853.
    Full references (including those not matched with items on IDEAS)

    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. Ismat Beg & Mujahid Abbas & Muhammad Waseem Asghar, 2023. "Approximation of the Solution of Split Equality Fixed Point Problem for Family of Multivalued Demicontractive Operators with Application," Mathematics, MDPI, vol. 11(4), pages 1-16, February.
    2. Truong Minh Tuyen & Nguyen Thi Thu Thuy & Nguyen Minh Trang, 2019. "A Strong Convergence Theorem for a Parallel Iterative Method for Solving the Split Common Null Point Problem in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 271-291, October.
    3. Wachirapong Jirakitpuwapat & Poom Kumam & Yeol Je Cho & Kanokwan Sitthithakerngkiet, 2019. "A General Algorithm for the Split Common Fixed Point Problem with Its Applications to Signal Processing," Mathematics, MDPI, vol. 7(3), pages 1-20, February.
    4. Nishu Gupta & Mihai Postolache & Ashish Nandal & Renu Chugh, 2021. "A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm," Mathematics, MDPI, vol. 9(4), pages 1-19, February.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:6:p:874-:d:767601. 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.