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On optimality of two adaptive choices for the parameter of Dai–Liao method

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Abstract

Orthonormal matrices are a class of well-conditioned matrices with the least spectral condition number. Here, at first it is shown that a recently proposed choice for parameter of the Dai–Liao nonlinear conjugate gradient method makes the search direction matrix as close as possible to an orthonormal matrix in the Frobenius norm. Then, conducting a brief singular value analysis, it is shown that another recently proposed choice for the Dai–Liao parameter improves spectral condition number of the search direction matrix. Thus, theoretical justifications of the two choices for the Dai–Liao parameter are enhanced. Finally, some comparative numerical results are reported.

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Acknowledgments

This research was supported by the Research Council of Semnan University. The author is grateful to Professor William W. Hager for providing the line search code. He also thanks the anonymous reviewers for their valuable comments and suggestions helped to improve the presentation.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box: 35195-363, Semnan, Iran

    Saman Babaie-Kafaki

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  1. Saman Babaie-Kafaki
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Correspondence to Saman Babaie-Kafaki.

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Babaie-Kafaki, S. On optimality of two adaptive choices for the parameter of Dai–Liao method. Optim Lett 10, 1789–1797 (2016). https://doi.org/10.1007/s11590-015-0965-5

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  • DOI: https://doi.org/10.1007/s11590-015-0965-5

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