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The Minkowski Theorem for Max-plus Convex Sets

Stephane Gaubert·Ricardo Katz
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Abstract

We establish the following max-plus analogue of Minkowski's theorem. Any point of a compact max-plus convex subset of $(R\cup\{-\infty\})^n$ can be written as the max-plus convex combination of at most $n+1$ of the extreme points of this subset. We establish related results for closed max-plus convex cones and closed unbounded max-plus convex sets. In particular, we show that a closed max-plus convex set can be decomposed as a max-plus sum of its recession cone and of the max-plus convex hull of its extreme points.

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Stephane Gaubert, Ricardo Katz. 2006-05-02. The Minkowski Theorem for Max-plus Convex Sets. https://doi.org/10.1016/j.laa.2006.09.019

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