The Minkowski Theorem for Max-plus Convex Sets - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports (Research Report) Year : 2006

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.
Fichier principal
Vignette du fichier
RR-5907.pdf (310.73 Ko) Télécharger le fichier

Dates and versions

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

Identifiers

  • HAL Id : inria-00071358 , version 1

Cite

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

Share

Gmail Facebook Twitter LinkedIn More