The Minkowski theorem for max-plus convex sets
- 作者：Sté ; phane Gaubert ; Ricardo D. Katz
- 关键词：Max-plus algebra ; Tropical algebra ; Extreme points ; Polyhedra ; Polytopes ; Convex cones ; Convex sets ; Abstract convexity ; Krein-milman theorem ; Caratheodory theorem
- 刊名：Linear Algebra and its Applications
- 出版年：2007
- 期刊代码：38_00243795
- 类别：mt
- 出版时间：1 March 2007
- 卷：421
- 期：2-3
- 页码：356-369
- 文件大小：211 K
摘要
We establish the following max-plus analogue of Minkowski’s theorem. Any point of a compact max-plus convex subset of 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.