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An active-set projected trust region algorithm for box constrained optimization problems

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Abstract

An active-set projected trust region algorithm is proposed for box constrained optimization problems, where the given algorithm is designed by three steps. First, the projected gradient direction which normally has better numerical performance is introduced. Second, the projected trust region direction that often possesses good convergence is defined, where the matrix of trust region subproblem is updated by limited memory strategy. Third, in order to get both good numerical performance and convergence, the authors define the final search which is the convex combination of the projected gradient direction and the projected trust region direction. Under suitable conditions, the global convergence of the given algorithm is established. Numerical results show that the presented method is competitive to other similar methods.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Guangxi University, Nanning, 530004, China

    Gonglin Yuan & Zengxin Wei

  2. School of Mathematic and Computing Science, Guilin University of Electronic Technology, Guilin, 541004, China

    Maojun Zhang

Authors
  1. Gonglin Yuan
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  2. Zengxin Wei
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  3. Maojun Zhang
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Corresponding author

Correspondence to Gonglin Yuan.

Additional information

This research was supported by Guangxi Natural Science Foundation under Grant Nos. 2012GXNSFAA053002 and 2012GXNSFAA053013, and the National Natural Science Foundation of China under Grant Nos. 11261006, 11161003, 71101033, and 71001015.

This paper was recommended for publication by Editor DAI Yuhong.

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Yuan, G., Wei, Z. & Zhang, M. An active-set projected trust region algorithm for box constrained optimization problems. J Syst Sci Complex 28, 1128–1147 (2015). https://doi.org/10.1007/s11424-014-2199-5

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  • DOI: https://doi.org/10.1007/s11424-014-2199-5

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