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A Modified Three-Term Conjugate Descent Derivative-Free Method for Constrained Nonlinear Monotone Equations and Signal Reconstruction Problems

Author

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  • Aliyu Yusuf

    (Department of Science, School of Continuing Education, Bayero University, BUK, Kano PMB 3011, Nigeria
    Department of Mathematical Sciences, Faculty of Science, Abubakar Tafawa Balewa University, Bauchi PMB 0248, Nigeria
    Numerical Optimization Research Group, Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano 700241, Nigeria)

  • Nibron Haggai Manjak

    (Department of Mathematical Sciences, Faculty of Science, Abubakar Tafawa Balewa University, Bauchi PMB 0248, Nigeria)

  • Maggie Aphane

    (Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria 0204, South Africa)

Abstract

Iterative methods for solving constraint nonlinear monotone equations have been developed and improved by many researchers. The aim of this research is to present a modified three-term conjugate descent (TTCD) derivative-free method for constrained nonlinear monotone equations. The proposed algorithm requires low storage memory; therefore, it has the capability to solve large-scale nonlinear equations. The algorithm generates a descent and bounded search direction d k at every iteration independent of the line search. The method is shown to be globally convergent under monotonicity and Lipschitz continuity conditions. Numerical results show that the suggested method can serve as an alternative to find the approximate solutions of nonlinear monotone equations. Furthermore, the method is promising for the reconstruction of sparse signal problems.

Suggested Citation

  • Aliyu Yusuf & Nibron Haggai Manjak & Maggie Aphane, 2024. "A Modified Three-Term Conjugate Descent Derivative-Free Method for Constrained Nonlinear Monotone Equations and Signal Reconstruction Problems," Mathematics, MDPI, vol. 12(11), pages 1-21, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1649-:d:1400994
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    References listed on IDEAS

    as
    1. Ibrahim Mohammed Sulaiman & Aliyu Muhammed Awwal & Maulana Malik & Nuttapol Pakkaranang & Bancha Panyanak, 2022. "A Derivative-Free MZPRP Projection Method for Convex Constrained Nonlinear Equations and Its Application in Compressive Sensing," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
    2. 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.
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