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The Minkowski theorem for max-plus convex sets

✍ Scribed by Stéphane Gaubert; Ricardo D. Katz

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
211 KB
Volume
421
Category
Article
ISSN
0024-3795

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✦ Synopsis

We establish the following max-plus analogue of Minkowski's theorem. Any point of a compact max-plus convex subset of (R ∪ {-∞}) 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 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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