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Reports (Research Report) Year : 2006

The Minkowski Theorem for Max-plus Convex Sets


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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inria-00071358 , version 1 (23-05-2006)


  • HAL Id : inria-00071358 , version 1


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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