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Some nonlinear conjugate gradient methods with sufficient descent condition and global convergence

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Abstract

In this paper, by taking a little modification to the search direction of the MPRP method, a variant PRP conjugate gradient method is proposed, which can satisfies the sufficient descent condition independent of any line search. Also, we propose a general form of conjugate gradient parameter \(\beta _k\), and the corresponding method always generates a sufficient descent direction independent of the line search employed. We establish the global convergence of our methods without the assumption that the steplength is bounded away from zero. Numerical results illustrate that our methods can efficiently solve the test problems and therefore is promising.

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Acknowledgments

We would like to thank Professors W. W. Hager and H. Zhang for their CG_DESCENT code for numerical comparison. This work is supported by the Natural Science Foundation of China (11361001), Doctor Foundation of Beifang University of Nationalities (2014XBZ09) and Fundamental Research Funds for the Central Universities (K50513100007).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710126, People’s Republic of China

    Xiao Liang Dong, Hongwei Liu & Yin Ling Xu

  2. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, People’s Republic of China

    Xi Mei Yang

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  1. Xiao Liang Dong
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  2. Hongwei Liu
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  3. Yin Ling Xu
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  4. Xi Mei Yang
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Correspondence to Xiao Liang Dong.

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Dong, X.L., Liu, H., Xu, Y.L. et al. Some nonlinear conjugate gradient methods with sufficient descent condition and global convergence. Optim Lett 9, 1421–1432 (2015). https://doi.org/10.1007/s11590-014-0836-5

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  • DOI: https://doi.org/10.1007/s11590-014-0836-5

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