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A simplicial branch-and-bound algorithm conscious of special structures in concave minimization problems

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Abstract

In this paper, we develop a simplicial branch-and-bound algorithm for generating globally optimal solutions to concave minimization problems with low rank nonconvex structures. We propose to remove all additional constraints imposed on the usual linear programming relaxed problem. Therefore, in each bounding operation, we solve a linear programming problem whose constraints are exactly the same as the target problem. Although the lower bound worsens as a natural consequence, we offset this weakness by using an inexpensive bound tightening procedure based on Lagrangian relaxation. After giving a proof of the convergence, we report a numerical comparison with existing algorithms.

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Authors and Affiliations

  1. Graduate School of System and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, 305-8573, Japan

    Takahito Kuno & Hidetoshi Nagai

Authors
  1. Takahito Kuno
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  2. Hidetoshi Nagai
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Correspondence to Takahito Kuno.

Additional information

T. Kuno was partially supported by the Grand-in-Aid for Scientific Research (C) 17560050 from the Japan Society for the Promotion of Sciences.

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Kuno, T., Nagai, H. A simplicial branch-and-bound algorithm conscious of special structures in concave minimization problems. Comput Optim Appl 39, 219–238 (2008). https://doi.org/10.1007/s10589-007-9068-2

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  • DOI: https://doi.org/10.1007/s10589-007-9068-2

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