On topological types of ordered median functions

J. Grzybowski, J. Kalcsics, S. Nickel, D. Pallaschke*, R. Urbański

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

An ordered median functions is a continuous piecewise-linear function. It is well known that in finite dimensional spaces every continuous piecewise-linear function admits a max-min representation in terms of its linear functions. An explicit representation of an ordered median function in max-min form is given by the authors and will appear in a forthcoming issue of this journal. Based on this representation, we give a topological classification of ordered median functions through their simplicial complex of ascent (resp. descent) cones.

Original languageEnglish
Pages (from-to)149-160
Number of pages12
JournalOptimization
Volume64
Issue number1
Early online date17 Feb 2014
DOIs
Publication statusPublished - 2 Jan 2015

Keywords

  • convex analysis
  • max-min representation
  • ordered median functions

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