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Supermodularity in Mean-Partition Problems*

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Abstract

Supermodularity of the λ function which defines a permutation polytope has proved to be crucial for the polytope to have some nice fundamental properties. Supermodularity has been established for the λ function for the sum-partition problem under various models. On the other hand, supermodularity has not been established for the mean-partition problem even for the most basic labeled single-shape model. In this paper, we fill this gap and also settle for all other models except one. We further extend our results to other types of supermodularity.

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Authors and Affiliations

  1. Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, P.R. China, 300

    F. H. Chang & F. K. Hwang

Authors
  1. F. H. Chang
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  2. F. K. Hwang
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Corresponding author

Correspondence to F. K. Hwang.

Additional information

*This research is partially supported by a Republic of China National Science grant NSC 92-2115-M-009-014.

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Chang, F.H., Hwang, F.K. Supermodularity in Mean-Partition Problems*. J Glob Optim 33, 337–347 (2005). https://doi.org/10.1007/s10898-004-7391-z

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  • DOI: https://doi.org/10.1007/s10898-004-7391-z

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