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A nonmonotone PSB algorithm for solving unconstrained optimization

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Abstract

PSB (Powell-Symmetric-Broyden) algorithm is a very important algorithm and has been extensively used in trust region methods. However, there are few studies on the line search type PSB algorithm. The primary reason is that the direction generated by this class of algorithms is not necessarily a descent direction of the objective function. In this paper, by combining a nonmonotone line search technique with the PSB method, we propose a nonmonotone PSB algorithm for solving unconstrained optimization. Under proper conditions, we establish global convergence and superlinear convergence of the proposed algorithm. At the same time we verify the efficiency of the proposed algorithm by some numerical experiments.

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, Hunan, China

    Jiao Li & Yu-Fei Yang

  2. College of Science, Hunan University of Technology, Zhuzhou, 412008, Hunan, China

    Bo Yu

Authors
  1. Jiao Li
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  2. Yu-Fei Yang
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  3. Bo Yu
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Corresponding author

Correspondence to Yu-Fei Yang.

Additional information

The work is supported in part by the NNSF of China (No. 60872129, 60835004) and the Science and Technology project of Hunan Province (No. 2009SK3027).

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Li, J., Yang, YF. & Yu, B. A nonmonotone PSB algorithm for solving unconstrained optimization. Comput Optim Appl 52, 267–280 (2012). https://doi.org/10.1007/s10589-011-9408-0

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  • DOI: https://doi.org/10.1007/s10589-011-9408-0

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