The Minkowski Theorem for Max-plus Convex Sets
| dc.creator | Gaubert, Stephane | |
| dc.creator | Katz, Ricardo | |
| dc.date | 2006-05-02 | |
| dc.date.accessioned | 2026-07-07T07:42:19Z | |
| dc.date.available | 2026-07-07T07:42:19Z | |
| dc.description | We establish the following max-plus analogue of Minkowski's theorem. Any point of a compact max-plus convex subset of $(R\cup\{-\infty\})^n$ 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. | |
| dc.description | 13 pages, 4 figures (5 eps files) | |
| dc.identifier | https://arxiv.org/abs/math/0605078 | |
| dc.identifier | http://arxiv.org/abs/math/0605078 | |
| dc.identifier | Linear Algebra and its Applications 421 (2007), 356--369. | |
| dc.identifier | doi:10.1016/j.laa.2006.09.019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122401 | |
| dc.subject | Metric Geometry | |
| dc.subject | Optimization and Control | |
| dc.subject | 52A01; 16Y60, 46A55 | |
| dc.title | The Minkowski Theorem for Max-plus Convex Sets | |
| dc.type | text |