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A Quadratic Hybridization of Polak–Ribière–Polyak and Fletcher–Reeves Conjugate Gradient Methods

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  • Saman Babaie-Kafaki

    (Semnan University
    Institute for Research in Fundamental Sciences (IPM))

Abstract

In order to take advantage of the attractive features of Polak–Ribière–Polyak and Fletcher–Reeves conjugate gradient methods, two hybridizations of these methods are suggested, using a quadratic relaxation of a hybrid conjugate gradient parameter proposed by Gilbert and Nocedal. In the suggested methods, the hybridization parameter is computed based on a conjugacy condition. Under proper conditions, it is shown that the proposed methods are globally convergent for general objective functions. Numerical results are reported; they demonstrate the efficiency of one of the proposed methods in the sense of the performance profile introduced by Dolan and Moré.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:3:d:10.1007_s10957-012-0016-7
    DOI: 10.1007/s10957-012-0016-7
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    References listed on IDEAS

    as
    1. N. Andrei, 2009. "Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 249-264, May.
    2. 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.
    3. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, June.
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    Cited by:

    1. Saman Babaie-Kafaki, 2015. "On Optimality of the Parameters of Self-Scaling Memoryless Quasi-Newton Updating Formulae," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 91-101, October.

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