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Spectral modified Polak–Ribiére–Polyak projection conjugate gradient method for solving monotone systems of nonlinear equations

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  • Awwal, Aliyu Muhammed
  • Kumam, Poom
  • Abubakar, Auwal Bala

Abstract

In this paper, we present a modification of Polak–Ribie´re–Polyak (PRP) conjugate gradient method for solving system of monotone nonlinear equations which is a combination of spectral conjugate gradient method and the hyperplane projection technique. The method is based on two methods for unconstrained optimization proposed by Wan et al. (2011) and Sun (2015). We obtained a new search direction by the use of a different formula for the conjugate gradient parameter. The search direction satisfies the sufficient descent condition and the global convergence of the method is established under some assumptions. Preliminary numerical comparison with some existing methods shows the efficiency of the proposed method.

Suggested Citation

  • Awwal, Aliyu Muhammed & Kumam, Poom & Abubakar, Auwal Bala, 2019. "Spectral modified Polak–Ribiére–Polyak projection conjugate gradient method for solving monotone systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    • Handle: RePEc:eee:apmaco:v:362:y:2019:i:c:31
    DOI: 10.1016/j.amc.2019.06.028
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    References listed on IDEAS

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    1. 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.
    2. G. Zhou & K. C. Toh, 2005. "Superlinear Convergence of a Newton-Type Algorithm for Monotone Equations," Journal of Optimization Theory and Applications, Springer, vol. 125(1), pages 205-221, April.
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    Cited by:

    1. Ibrahim Mohammed Sulaiman & Aliyu Muhammed Awwal & Maulana Malik & Nuttapol Pakkaranang & Bancha Panyanak, 2022. "A Derivative-Free MZPRP Projection Method for Convex Constrained Nonlinear Equations and Its Application in Compressive Sensing," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
    2. Rabiu Bashir Yunus & Nooraini Zainuddin & Hanita Daud & Ramani Kannan & Samsul Ariffin Abdul Karim & Mahmoud Muhammad Yahaya, 2023. "A Modified Structured Spectral HS Method for Nonlinear Least Squares Problems and Applications in Robot Arm Control," Mathematics, MDPI, vol. 11(14), pages 1-17, July.
    3. Kin Keung Lai & Shashi Kant Mishra & Bhagwat Ram & Ravina Sharma, 2023. "A Conjugate Gradient Method: Quantum Spectral Polak–Ribiére–Polyak Approach for Unconstrained Optimization Problems," Mathematics, MDPI, vol. 11(23), pages 1-14, December.

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