Reduced Pairs of Compact Convex Sets and Ordered Median Functions

Jerzy Grzybowski (), Diethard Pallaschke () and Ryszard Urbański ()
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Jerzy Grzybowski: Adam Mickiewicz University
Diethard Pallaschke: University of Karlsruhe – KIT
Ryszard Urbański: Adam Mickiewicz University

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 2, No 2, 354-364

Abstract: Abstract 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.

Keywords: Minkowski duality; Reduced pairs of compact convex sets; Piecewise linear functions; 26B25; 52A07; 52A20 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-015-0860-3

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