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A Solution Method for Nonlinear Monotone Equations via Hybrid Spectral Conjugate Gradient and Signal Recovery Problems

Author

Listed:
  • Aliyu Yusuf

    (Bayero University Kano
    Abubakar Tafawa Balewa University Bauchi
    Bayero University Kano)

  • Nibron Haggai Manjak

    (Abubakar Tafawa Balewa University Bauchi)

  • Hassan Mohammad

    (Bayero University Kano)

  • Aliyu Ibrahim Kiri

    (Bayero University Kano)

  • Auwal Bala Abubakar

    (Bayero University Kano
    Sefako Makgatho Health Sciences University
    Kyungpook National University)

Abstract

In this paper, we propose a method via hybrid spectral conjugate gradient to solve nonlinear monotone equations and signal recovery problems. This has been done using the hybrid conjugate gradient (CG) parameters of Dai-Yuan (DY), conjugate descent (CD), Hestenes-Stiefel (HS), Liu-Storey (LS) and the corresponding search direction of spectral conjugate gradient method. The search direction has proved to be adequately descent regardless of the step-size. Under reasonable assumptions, the convergence of the algorithm is established. Additionally, numerical tests are run on a set of benchmark test problems to illustrate the effectiveness and competitiveness of the new algorithm compared with other existing alternatives. Finally, some applications of the proposed algorithm are explored.

Suggested Citation

  • Aliyu Yusuf & Nibron Haggai Manjak & Hassan Mohammad & Aliyu Ibrahim Kiri & Auwal Bala Abubakar, 2024. "A Solution Method for Nonlinear Monotone Equations via Hybrid Spectral Conjugate Gradient and Signal Recovery Problems," SN Operations Research Forum, Springer, vol. 5(2), pages 1-16, June.
    • Handle: RePEc:spr:snopef:v:5:y:2024:i:2:d:10.1007_s43069-024-00326-8
    DOI: 10.1007/s43069-024-00326-8
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    References listed on IDEAS

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    1. Gao, Peiting & He, Chuanjiang & Liu, Yang, 2019. "An adaptive family of projection methods for constrained monotone nonlinear equations with applications," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 1-16.
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