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An Efficient Conjugate Gradient Method for Convex Constrained Monotone Nonlinear Equations with Applications

Author

Listed:
  • Auwal Bala Abubakar

    (KMUTTFixed Point Research Laboratory, SCL 802 Fixed Point Laboratory, Science Laboratory Building, 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, SCL 802 Fixed Point Laboratory, Science Laboratory Building, 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
    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
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

  • Hassan Mohammad

    (Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano 700241, Nigeria)

  • Aliyu Muhammed Awwal

    (KMUTTFixed Point Research Laboratory, SCL 802 Fixed Point Laboratory, Science Laboratory Building, 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)

Abstract

This research paper proposes a derivative-free method for solving systems of nonlinear equations with closed and convex constraints, where the functions under consideration are continuous and monotone. Given an initial iterate, the process first generates a specific direction and then employs a line search strategy along the direction to calculate a new iterate. If the new iterate solves the problem, the process will stop. Otherwise, the projection of the new iterate onto the closed convex set (constraint set) determines the next iterate. In addition, the direction satisfies the sufficient descent condition and the global convergence of the method is established under suitable assumptions. Finally, some numerical experiments were presented to show the performance of the proposed method in solving nonlinear equations and its application in image recovery problems.

Suggested Citation

  • Auwal Bala Abubakar & Poom Kumam & Hassan Mohammad & Aliyu Muhammed Awwal, 2019. "An Efficient Conjugate Gradient Method for Convex Constrained Monotone Nonlinear Equations with Applications," Mathematics, MDPI, vol. 7(9), pages 1-25, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:767-:d:259574
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    Citations

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    Cited by:

    1. Najib Ullah & Abdullah Shah & Jamilu Sabi’u & Xiangmin Jiao & Aliyu Muhammed Awwal & Nuttapol Pakkaranang & Said Karim Shah & Bancha Panyanak, 2023. "A One-Parameter Memoryless DFP Algorithm for Solving System of Monotone Nonlinear Equations with Application in Image Processing," Mathematics, MDPI, vol. 11(5), pages 1-26, March.

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