Journal of Global Optimization

, Volume 33, Issue 3, pp 337–347 | Cite as

Supermodularity in Mean-Partition Problems*

  • F. H. Chang
  • F. K. Hwang


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.


mean-partition supermodular 


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  1. 1.
    Anily, S., Federgruen, A. 1991Structured partition problemsOperational Research39130149Google Scholar
  2. 2.
    Gao, B., Hwang, F.K., Li, W.W-C., Rothblum, U.G. 1999Partition polytopes over 1-dimensional pointsMathematical Programming85335362CrossRefGoogle Scholar
  3. 3.
    Hwang, F.K., Lee, J.S., Rothblum, U.G. 2004Permutation polytopes corresponding to strongly supermodular functionsDiscrete Applied Mathematics1425297CrossRefGoogle Scholar
  4. 4.
    Hwang, F.K., Liao, M.M., Chen, C.Y. 2000Supermodularity of various partition problemsJournal of Global Optimization18275282CrossRefGoogle Scholar
  5. 5.
    Hwang, F.K., Rothblum, U.G. 1996Directional-quasi-convexity, asymmetric Schur-convexity and optionality of consecutive partitionsMathematics Operational Research21540554Google Scholar
  6. 6.
    Shapely, L.S. 1971Cores of convex gormesInternational Journal of Game Theory11129Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Applied MathematicsNational Chiao Tung UniversityHsinchuP.R. China

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