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A Modified Fletcher–Reeves Conjugate Gradient Method for Monotone Nonlinear Equations with Some Applications

Author

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  • 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)

  • Kanokwan Sitthithakerngkiet

    (Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, 1518 Pracharat 1 Road, Wongsawang, Bangsue, Bangkok 10800, Thailand)

Abstract

One of the fastest growing and efficient methods for solving the unconstrained minimization problem is the conjugate gradient method (CG). Recently, considerable efforts have been made to extend the CG method for solving monotone nonlinear equations. In this research article, we present a modification of the Fletcher–Reeves (FR) conjugate gradient projection method for constrained monotone nonlinear equations. The method possesses sufficient descent property and its global convergence was proved using some appropriate assumptions. Two sets of numerical experiments were carried out to show the good performance of the proposed method compared with some existing ones. The first experiment was for solving monotone constrained nonlinear equations using some benchmark test problem while the second experiment was applying the method in signal and image recovery problems arising from compressive sensing.

Suggested Citation

  • Auwal Bala Abubakar & Poom Kumam & Hassan Mohammad & Aliyu Muhammed Awwal & Kanokwan Sitthithakerngkiet, 2019. "A Modified Fletcher–Reeves Conjugate Gradient Method for Monotone Nonlinear Equations with Some Applications," Mathematics, MDPI, vol. 7(8), pages 1-25, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:745-:d:257949
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    References listed on IDEAS

    as
    1. Zhou, Weijun & Wang, Fei, 2015. "A PRP-based residual method for large-scale monotone nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 1-7.
    2. Papp, Zoltan & Rapajić, Sanja, 2015. "FR type methods for systems of large-scale nonlinear monotone equations," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 816-823.
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    Cited by:

    1. Abubakar, Auwal Bala & Kumam, Poom & Ibrahim, Abdulkarim Hassan & Chaipunya, Parin & Rano, Sadiya Ali, 2022. "New hybrid three-term spectral-conjugate gradient method for finding solutions of nonlinear monotone operator equations with applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 670-683.
    2. Elena Tovbis & Vladimir Krutikov & Predrag Stanimirović & Vladimir Meshechkin & Aleksey Popov & Lev Kazakovtsev, 2023. "A Family of Multi-Step Subgradient Minimization Methods," Mathematics, MDPI, vol. 11(10), pages 1-24, May.

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