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An Improved Spectral Conjugate Gradient Algorithm for Nonconvex Unconstrained Optimization Problems

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Abstract

In this paper, an improved spectral conjugate gradient algorithm is developed for solving nonconvex unconstrained optimization problems. Different from the existent methods, the spectral and conjugate parameters are chosen such that the obtained search direction is always sufficiently descent as well as being close to the quasi-Newton direction. With these suitable choices, the additional assumption in the method proposed by Andrei on the boundedness of the spectral parameter is removed. Under some mild conditions, global convergence is established. Numerical experiments are employed to demonstrate the efficiency of the algorithm for solving large-scale benchmark test problems, particularly in comparison with the existent state-of-the-art algorithms available in the literature.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant No. 71071162, 70921001, 71210003).

The authors would like to express their thanks to the three anonymous referees for their constructive comments on the paper, which have greatly improved its presentation.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, China

    Songhai Deng & Zhong Wan

  2. School of Business, Central South University, Changsha, China

    Xiaohong Chen

Authors
  1. Songhai Deng
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  2. Zhong Wan
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  3. Xiaohong Chen
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Corresponding author

Correspondence to Zhong Wan.

Additional information

Communicated by Kok Lay Teo.

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Deng, S., Wan, Z. & Chen, X. An Improved Spectral Conjugate Gradient Algorithm for Nonconvex Unconstrained Optimization Problems. J Optim Theory Appl 157, 820–842 (2013). https://doi.org/10.1007/s10957-012-0239-7

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  • DOI: https://doi.org/10.1007/s10957-012-0239-7

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