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Global convergence in a hybrid conjugate gradient projection method for finding solutions of constrained nonlinear equations with applications

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  • Yan Xia
  • Dandan Li
  • Songhua Wang

Abstract

In this paper, a hybrid conjugate gradient projection method for finding solutions of constrained nonlinear equations is proposed by integrating both hyperplane projection and hybrid techniques. The key features of this method are as follows: (1) It is characterized by a low storage requirement and relies solely on function values; (2) The designed search direction ensures the sufficient descent property without the need for line search approaches; (3) Under certain reasonable assumptions, the global convergence of the method is established; (4) Experimental results demonstrate that the proposed method outperforms the two existing methods about 75.71%, 85.36%, and 86.43% of benchmark problems in terms of CPU time, the number of function evaluations, and iterations. Furthermore, it is applied to successfully solve the sparse signal restoration problems.

Suggested Citation

  • Yan Xia & Dandan Li & Songhua Wang, 2025. "Global convergence in a hybrid conjugate gradient projection method for finding solutions of constrained nonlinear equations with applications," PLOS ONE, Public Library of Science, vol. 20(10), pages 1-22, October.
    • Handle: RePEc:plo:pone00:0335265
    DOI: 10.1371/journal.pone.0335265
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    References listed on IDEAS

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    1. Dai, Zhifeng & Zhou, Huiting & Wen, Fenghua & He, Shaoyi, 2020. "Efficient predictability of stock return volatility: The role of stock market implied volatility," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    2. 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.
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