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A Sufficiently Descending Three-Term Nonlinear Conjugate Gradient Method for Unconstrained Optimization Problems with Application

Author

Listed:
  • Aliyu M. Awwal

    (Gombe State University (GSU)
    Universiti Sultan Zainal Abidin
    Gombe State University)

  • Sulaiman M. Ibrahim

    (Universiti Utara Malaysia
    Faculty of Education and Arts Sohar University)

  • Issam A. R. Moghrabi

    (Information Systems and Technology Depart.. Kuwait Technical College)

  • Aceng Sambas

    (Universiti Sultan Zainal Abidin)

  • Rosshairy Abd Rahman

    (Universiti Utara Malaysia)

  • Semiu O. Oladejo

    (Gombe State University (GSU)
    Gombe State University)

Abstract

This paper presents a new nonlinear conjugate gradient method in which the new search direction comprises three terms, and the step length is required to satisfy the well-known strong Wolfe line search strategy. The new three-term search direction is a modification of a recently published one in the literature. Unlike the search direction that was modified, the new search direction satisfies the important sufficient descent condition without imposing additional conditions or restrictions. We discuss the convergence results of the proposed method under the assumption that the function is smooth and its gradient is Lipschitz continuous. We present numerical experiments on a collection of benchmark test problems and compare the new method’s performance with some existing ones. Finally, we apply the method to robotic arm motion control.

Suggested Citation

  • Aliyu M. Awwal & Sulaiman M. Ibrahim & Issam A. R. Moghrabi & Aceng Sambas & Rosshairy Abd Rahman & Semiu O. Oladejo, 2025. "A Sufficiently Descending Three-Term Nonlinear Conjugate Gradient Method for Unconstrained Optimization Problems with Application," SN Operations Research Forum, Springer, vol. 6(3), pages 1-25, September.
    • Handle: RePEc:spr:snopef:v:6:y:2025:i:3:d:10.1007_s43069-025-00493-2
    DOI: 10.1007/s43069-025-00493-2
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    References listed on IDEAS

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    1. Sulaiman M Ibrahim & Lawal Muhammad & Rabiu Bashir Yunus & Muhammad Yusuf Waziri & Saadi bin Ahmad Kamaruddin & Aceng Sambas & Nooraini Zainuddin & Ali F Jameel, 2025. "The global convergence of some self-scaling conjugate gradient methods for monotone nonlinear equations with application to 3DOF arm robot model," PLOS ONE, Public Library of Science, vol. 20(1), pages 1-36, January.
    2. Salihu, Nasiru & Kumam, Poom & Sulaiman, Ibrahim Mohammed & Arzuka, Ibrahim & Kumam, Wiyada, 2024. "An efficient Newton-like conjugate gradient method with restart strategy and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 354-372.
    3. Nasiru Salihu & Poom Kumam & Aliyu Muhammed Awwal & Ibrahim Mohammed Sulaiman & Thidaporn Seangwattana, 2023. "The global convergence of spectral RMIL conjugate gradient method for unconstrained optimization with applications to robotic model and image recovery," PLOS ONE, Public Library of Science, vol. 18(3), pages 1-19, March.
    4. Min Sun & Jing Liu & Yaru Wang, 2020. "Two Improved Conjugate Gradient Methods with Application in Compressive Sensing and Motion Control," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-11, May.
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