# The Minkowski Theorem for Max-plus Convex Sets

Abstract : We establish the following max-plus analogue of Minkowski's theorem. Any point of a compact max-plus convex subset of $(\mathbbR\cup{-\infty})^n$ 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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https://hal.inria.fr/inria-00071358
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Submitted on : Tuesday, May 23, 2006 - 4:51:14 PM
Last modification on : Friday, February 4, 2022 - 3:13:50 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:06:36 PM

### Identifiers

• HAL Id : inria-00071358, version 1

### Citation

Stéphane Gaubert, Ricardo David Katz. The Minkowski Theorem for Max-plus Convex Sets. [Research Report] RR-5907, INRIA. 2006. ⟨inria-00071358⟩

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