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An optimal parameter choice for the Dai–Liao family of conjugate gradient methods by avoiding a direction of the maximum magnification by the search direction matrix

Author

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  • Zohre Aminifard

    (Semnan University)

  • Saman Babaie-Kafaki

    (Semnan University)

Abstract

Based on a singular value analysis conducted on the Dai–Liao conjugate gradient method, it is shown that when the gradient approximately lies in the direction of the maximum magnification by the search direction matrix, the method may get into some computational errors and also, the convergence may occur hardly. Hence, we obtain a formula for computing the Dai–Liao parameter which makes the direction of the maximum magnification by the search direction matrix to be orthogonal to the gradient. We briefly discuss global convergence of the corresponding Dai–Liao method with and without convexity assumption on the objective function. Numerical experiments on a set of test problems of the CUTEr collection show practical effectiveness of the suggested adaptive choice of the Dai–Liao parameter in the sense of the Dolan–Moré performance profile.

Suggested Citation

  • Zohre Aminifard & Saman Babaie-Kafaki, 2019. "An optimal parameter choice for the Dai–Liao family of conjugate gradient methods by avoiding a direction of the maximum magnification by the search direction matrix," 4OR, Springer, vol. 17(3), pages 317-330, September.
    • Handle: RePEc:spr:aqjoor:v:17:y:2019:i:3:d:10.1007_s10288-018-0387-1
    DOI: 10.1007/s10288-018-0387-1
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    References listed on IDEAS

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    1. Avinoam Perry, 1976. "A Modified Conjugate Gradient Algorithm," Discussion Papers 229, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. M. Fatemi, 2016. "An Optimal Parameter for Dai–Liao Family of Conjugate Gradient Methods," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 587-605, May.
    3. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, June.
    4. Babaie-Kafaki, Saman & Ghanbari, Reza, 2014. "The Dai–Liao nonlinear conjugate gradient method with optimal parameter choices," European Journal of Operational Research, Elsevier, vol. 234(3), pages 625-630.
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    Cited by:

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