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A One-Parameter Memoryless DFP Algorithm for Solving System of Monotone Nonlinear Equations with Application in Image Processing

Author

Listed:
  • Najib Ullah

    (Department of Mathematics, COMSATS University Islamabad, Park Road, Islamabad 45550, Pakistan
    Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York, NY 11794, USA)

  • Abdullah Shah

    (Department of Mathematics, College of Computing and Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

  • Jamilu Sabi’u

    (Department of Mathematics, Yusuf Maitama Sule University, Kano 700282, Nigeria)

  • Xiangmin Jiao

    (Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York, NY 11794, USA)

  • Aliyu Muhammed Awwal

    (Department of Mathematics, Faculty of Science, Gombe State University (GSU), Gombe 760214, Nigeria
    GSU-Mathematics for Innovative Research Group, Gombe State University (GSU), Gombe 760214, Nigeria)

  • Nuttapol Pakkaranang

    (Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand)

  • Said Karim Shah

    (Department of Physics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan)

  • Bancha Panyanak

    (Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

Abstract

In matrix analysis, the scaling technique reduces the chances of an ill-conditioning of the matrix. This article proposes a one-parameter scaling memoryless Davidon–Fletcher–Powell (DFP) algorithm for solving a system of monotone nonlinear equations with convex constraints. The measure function that involves all the eigenvalues of the memoryless DFP matrix is minimized to obtain the scaling parameter’s optimal value. The resulting algorithm is matrix and derivative-free with low memory requirements and is globally convergent under some mild conditions. A numerical comparison showed that the algorithm is efficient in terms of the number of iterations, function evaluations, and CPU time. The performance of the algorithm is further illustrated by solving problems arising from image restoration.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1221-:d:1085754
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    References listed on IDEAS

    as
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    9. 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.
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    Cited by:

    1. Dandan Li & Yong Li & Songhua Wang, 2024. "An Improved Three-Term Conjugate Gradient Algorithm for Constrained Nonlinear Equations under Non-Lipschitz Conditions and Its Applications," Mathematics, MDPI, vol. 12(16), pages 1-22, August.

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