Reduced Pairs of Compact Convex Sets and Ordered Median Functions

Reduced Pairs of Compact Convex Sets and Ordered Median Functions

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Article ID: iaor20163664
Volume: 171
Issue: 2
Start Page Number: 354
End Page Number: 364
Publication Date: Nov 2016
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: programming: convex
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.

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