Journal of Optimization Theory and Applications

, Volume 171, Issue 2, pp 354–364 | Cite as

Reduced Pairs of Compact Convex Sets and Ordered Median Functions

  • Jerzy Grzybowski
  • Diethard Pallaschke
  • Ryszard Urbański


We prove that in finite dimensional spaces every ordered median function is the Minkowski dual of a reduced pair of polytopes. This implies a very general theorem on the representation of an ordered median function as a uniquely determined difference of two sublinear functions up to adding and subtracting one and the same arbitrary sublinear function.


Minkowski duality Reduced pairs of compact convex sets Piecewise linear functions 

Mathematics Subject Classification

26B25 52A07 52A20 


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Jerzy Grzybowski
    • 1
  • Diethard Pallaschke
    • 2
  • Ryszard Urbański
    • 1
  1. 1.Adam Mickiewicz UniversityPoznańPoland
  2. 2.University of Karlsruhe – KITKarlsruheGermany

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