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A Version of Bundle Trust Region Method with Linear Programming

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Abstract

We present a general version of bundle trust region method for minimizing convex functions. The trust region is constructed by generic \(p\)-norm with \(p\in [1,+\infty ]\). In each iteration the algorithm solves a subproblem with a constraint involving \(p\)-norm. We show the convergence of the generic bundle trust region algorithm. In implementation, the infinity norm is chosen so that a linear programming subproblem is solved in each iteration. Preliminary numerical experiments show that our algorithm performs comparably with the traditional bundle trust region method and has advantages in solving large-scale problems.

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Data Availability Statement

The codes of the algorithm developed in this study are available in the Bitbucket repository https://bitbucket.org/shuai_liu_leo/bundletrustregionlp/src/master/. The other datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.

Notes

  1. https://cs.nyu.edu/~overton/software/hanso/

  2. https://bitbucket.org/shuai_liu_leo/bundletrustregionlp/src/master/

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Authors and Affiliations

  1. School of Software, South China Normal University Nanhai Campus, Foshan, Guangdong, China

    Shuai Liu

  2. School of Science, Royal Melbourne Institute of Technology, 124 La Trobe St, Melbourne, VIC, 3000, Australia

    Andrew C. Eberhard & Yousong Luo

Authors
  1. Shuai Liu
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  2. Andrew C. Eberhard
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  3. Yousong Luo
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Correspondence to Shuai Liu.

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Communicated by Shoham Sabach.

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The research of the first author was supported by the National Natural Science Foundation of China (Grant No. 12001208). The research of the second author was supported by the Australian Research Council (Grant No. DP120100567).

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Liu, S., Eberhard, A.C. & Luo, Y. A Version of Bundle Trust Region Method with Linear Programming. J Optim Theory Appl 199, 639–662 (2023). https://doi.org/10.1007/s10957-023-02293-2

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