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A Modified Self-Adaptive Conjugate Gradient Method for Solving Convex Constrained Monotone Nonlinear Equations for Signal Recovery Problems

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  • Auwal Bala Abubakar

    (KMUTTFixed Point Research Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano 700241, Nigeria)

  • Poom Kumam

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

  • Aliyu Muhammed Awwal

    (KMUTTFixed Point Research Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Department of Mathematics, Faculty of Science, Gombe State University, Gombe 760214, Nigeria)

  • Phatiphat Thounthong

    (Renewable Energy Research Centre, Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok, 1518 Pracharat 1 Road, Bangsue, Bangkok 10800, Thailand)

Abstract

In this article, we propose a modified self-adaptive conjugate gradient algorithm for handling nonlinear monotone equations with the constraints being convex. Under some nice conditions, the global convergence of the method was established. Numerical examples reported show that the method is promising and efficient for solving monotone nonlinear equations. In addition, we applied the proposed algorithm to solve sparse signal reconstruction problems.

Suggested Citation

  • Auwal Bala Abubakar & Poom Kumam & Aliyu Muhammed Awwal & Phatiphat Thounthong, 2019. "A Modified Self-Adaptive Conjugate Gradient Method for Solving Convex Constrained Monotone Nonlinear Equations for Signal Recovery Problems," Mathematics, MDPI, vol. 7(8), pages 1-24, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:693-:d:253969
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    References listed on IDEAS

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    1. Kaori Sugiki & Yasushi Narushima & Hiroshi Yabe, 2012. "Globally Convergent Three-Term Conjugate Gradient Methods that Use Secant Conditions and Generate Descent Search Directions for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 733-757, June.
    2. Chuanwei Wang & Yiju Wang & Chuanliang Xu, 2007. "A projection method for a system of nonlinear monotone equations with convex constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(1), pages 33-46, August.
    3. Mehiddin Al-Baali & Yasushi Narushima & Hiroshi Yabe, 2015. "A family of three-term conjugate gradient methods with sufficient descent property for unconstrained optimization," Computational Optimization and Applications, Springer, vol. 60(1), pages 89-110, January.
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