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A new class of nonlinear conjugate gradient coefficients with exact and inexact line searches

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  • Rivaie, Mohd
  • Mamat, Mustafa
  • Abashar, Abdelrhaman

Abstract

Conjugate gradient (CG) methods have played an important role in solving large-scale unconstrained optimization. In this paper, we propose a new family of CG coefficients (βk) that possess sufficient descent conditions and global convergence properties. This new βk is an extension of the already proven βkRMIL from Rivaie et al. [19] (A new class of nonlinear conjugate gradient coefficient with global convergence properties, Appl. Math. Comp. 218(2012) 11323-11332). Global convergence result is established using both exact and inexact line searches. Numerical results show that the performance of the new proposed formula is quite similar to βkRMIL and suited to both line searches. Importantly, the performance of this βk is more efficient and superior than the other well-known βk.

Suggested Citation

  • Rivaie, Mohd & Mamat, Mustafa & Abashar, Abdelrhaman, 2015. "A new class of nonlinear conjugate gradient coefficients with exact and inexact line searches," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1152-1163.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:1152-1163
    DOI: 10.1016/j.amc.2015.07.019
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    References listed on IDEAS

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    1. Jie Sun & Jiapu Zhang, 2001. "Global Convergence of Conjugate Gradient Methods without Line Search," Annals of Operations Research, Springer, vol. 103(1), pages 161-173, March.
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    Cited by:

    1. Siti Farhana Husin & Mustafa Mamat & Mohd Asrul Hery Ibrahim & Mohd Rivaie, 2020. "An Efficient Three-Term Iterative Method for Estimating Linear Approximation Models in Regression Analysis," Mathematics, MDPI, vol. 8(6), pages 1-12, June.
    2. 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.
    3. 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.
    4. Mrad, Hatem & Fakhari, Seyyed Mojtaba, 2024. "Optimization of unconstrained problems using a developed algorithm of spectral conjugate gradient method calculation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 282-290.

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