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A PRP-based residual method for large-scale monotone nonlinear equations

Author

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  • Zhou, Weijun
  • Wang, Fei

Abstract

This paper presents a derivative-free residual method for solving large-scale monotone nonlinear equations which may be nonsmooth. The method is constructed by replacing the gradients of the unmodified Polak–Ribière–Polyak (PRP) nonlinear conjugate gradient method with the residuals and combining the hyperplane projection technique. Under suitable conditions, we show that the proposed method converges globally in the sense that the whole iterative sequence converges to a solution of the problem. Some numerical results are reported to show its efficiency.

Suggested Citation

  • Zhou, Weijun & Wang, Fei, 2015. "A PRP-based residual method for large-scale monotone nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 1-7.
    • Handle: RePEc:eee:apmaco:v:261:y:2015:i:c:p:1-7
    DOI: 10.1016/j.amc.2015.03.069
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    Cited by:

    1. 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.
    2. Waziri, Mohammed Yusuf & Ahmed, Kabiru & Sabi’u, Jamilu, 2019. "A family of Hager–Zhang conjugate gradient methods for system of monotone nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 645-660.
    3. Jiang, Ling & Cao, Jinde & Xiong, Lianglin, 2019. "Generalized multiobjective robustness and relations to set-valued optimization," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 599-608.

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