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A family of Hager–Zhang conjugate gradient methods for system of monotone nonlinear equations

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  • Waziri, Mohammed Yusuf
  • Ahmed, Kabiru
  • Sabi’u, Jamilu

Abstract

This paper presents two modified Hager–Zhang (HZ) Conjugate Gradient methods for solving large-scale system of monotone nonlinear equations. The methods were developed by combining modified forms of the one-parameter method by Hager and Zhang (2006) and the hyperplane projection technique. Global convergence and numerical results of the methods are established. Preliminary numerical results show that the proposed methods are promising and more efficient compared to the methods presented by Mushtak and Keyvan (2018) and Sun et al. (2017).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:645-660
    DOI: 10.1016/j.amc.2019.06.012
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    References listed on IDEAS

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    1. J. Z. Zhang & N. Y. Deng & L. H. Chen, 1999. "New Quasi-Newton Equation and Related Methods for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 147-167, July.
    2. Mohammed Yusuf Waziri & Jamilu Sabi’u, 2015. "A Derivative-Free Conjugate Gradient Method and Its Global Convergence for Solving Symmetric Nonlinear Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-8, September.
    3. Dai, Zhifeng & Chen, Xiaohong & Wen, Fenghua, 2015. "A modified Perry’s conjugate gradient method-based derivative-free method for solving large-scale nonlinear monotone equations," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 378-386.
    4. 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.
    5. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, September.
    6. Avinoam Perry, 1978. "Technical Note—A Modified Conjugate Gradient Algorithm," Operations Research, INFORMS, vol. 26(6), pages 1073-1078, December.
    7. Weijun Zhou & Dongmei Shen, 2015. "Convergence Properties of an Iterative Method for Solving Symmetric Non-linear Equations," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 277-289, January.
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    Cited by:

    1. Branislav Ivanov & Gradimir V. Milovanović & Predrag S. Stanimirović, 2023. "Accelerated Dai-Liao projection method for solving systems of monotone nonlinear equations with application to image deblurring," Journal of Global Optimization, Springer, vol. 85(2), pages 377-420, February.
    2. Halilu, Abubakar Sani & Majumder, Arunava & Waziri, Mohammed Yusuf & Ahmed, Kabiru, 2021. "Signal recovery with convex constrained nonlinear monotone equations through conjugate gradient hybrid approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 520-539.

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