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Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization

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  • N. Andrei

    (Center for Advanced Modeling and Optimization)

Abstract

In this paper a new hybrid conjugate gradient algorithm is proposed and analyzed. The parameter β k is computed as a convex combination of the Polak-Ribière-Polyak and the Dai-Yuan conjugate gradient algorithms, i.e. β k N =(1−θ k )β k PRP +θ k β k DY . The parameter θ k in the convex combination is computed in such a way that the conjugacy condition is satisfied, independently of the line search. The line search uses the standard Wolfe conditions. The algorithm generates descent directions and when the iterates jam the directions satisfy the sufficient descent condition. Numerical comparisons with conjugate gradient algorithms using a set of 750 unconstrained optimization problems, some of them from the CUTE library, show that this hybrid computational scheme outperforms the known hybrid conjugate gradient algorithms.

Suggested Citation

  • N. Andrei, 2009. "Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 249-264, May.
    • Handle: RePEc:spr:joptap:v:141:y:2009:i:2:d:10.1007_s10957-008-9505-0
    DOI: 10.1007/s10957-008-9505-0
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    References listed on IDEAS

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    1. Y.H. Dai & Y. Yuan, 2001. "An Efficient Hybrid Conjugate Gradient Method for Unconstrained Optimization," Annals of Operations Research, Springer, vol. 103(1), pages 33-47, March.
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    Cited by:

    1. Saman Babaie-Kafaki, 2012. "A Quadratic Hybridization of Polak–Ribière–Polyak and Fletcher–Reeves Conjugate Gradient Methods," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 916-932, September.
    2. Yu, Yang & Wang, Yu & Deng, Rui & Yin, Yu, 2023. "New DY-HS hybrid conjugate gradient algorithm for solving optimization problem of unsteady partial differential equations with convection term," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 677-701.
    3. Jinbao Jian & Lin Yang & Xianzhen Jiang & Pengjie Liu & Meixing Liu, 2020. "A Spectral Conjugate Gradient Method with Descent Property," Mathematics, MDPI, vol. 8(2), pages 1-13, February.
    4. Zhifeng Dai, 2017. "Comments on Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 286-291, October.

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