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New hybrid three-term spectral-conjugate gradient method for finding solutions of nonlinear monotone operator equations with applications

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  • Abubakar, Auwal Bala
  • Kumam, Poom
  • Ibrahim, Abdulkarim Hassan
  • Chaipunya, Parin
  • Rano, Sadiya Ali

Abstract

In this paper, we present a new hybrid spectral-conjugate gradient (SCG) algorithm for finding approximate solutions to nonlinear monotone operator equations. The hybrid conjugate gradient parameter has the Polak–Ribière–Polyak (PRP), Dai–Yuan (DY), Hestenes–Stiefel (HS) and Fletcher–Reeves (FR) as special cases. Moreover, the spectral parameter is selected such that the search direction has the descent property. Also, the search directions are bounded and the sequence of iterates generated by the new hybrid algorithm converge globally. Furthermore, numerical experiments were conducted on some benchmark nonlinear monotone operator equations to assess the efficiency of the proposed algorithm. Finally, the algorithm is shown to have the ability to recover disturbed signals.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:201:y:2022:i:c:p:670-683
    DOI: 10.1016/j.matcom.2021.07.005
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    References listed on IDEAS

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    1. Dai, Zhifeng & Dong, Xiaodi & Kang, Jie & Hong, Lianying, 2020. "Forecasting stock market returns: New technical indicators and two-step economic constraint method," The North American Journal of Economics and Finance, Elsevier, vol. 53(C).
    2. Berry, Michael W. & Browne, Murray & Langville, Amy N. & Pauca, V. Paul & Plemmons, Robert J., 2007. "Algorithms and applications for approximate nonnegative matrix factorization," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 155-173, September.
    3. 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.
    4. Auwal Bala Abubakar & Kanikar Muangchoo & Auwal Muhammad & Abdulkarim Hassan Ibrahim, 2020. "A Spectral Gradient Projection Method for Sparse Signal Reconstruction in Compressive Sensing," Modern Applied Science, Canadian Center of Science and Education, vol. 14(5), pages 1-86, May.
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    Cited by:

    1. Jing, Shaoxue, 2023. "Time-delay Hammerstein system identification using modified cross-correlation method and variable stacking length multi-error algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 288-300.

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