Max-plus convex sets and functions
| dc.creator | Cohen, Guy | |
| dc.creator | Gaubert, Stephane | |
| dc.creator | Quadrat, Jean-Pierre | |
| dc.creator | Singer, Ivan | |
| dc.date | 2003-08-18 | |
| dc.date | 2004-02-16 | |
| dc.date.accessioned | 2026-07-07T05:00:27Z | |
| dc.date.available | 2026-07-07T05:00:27Z | |
| dc.description | We consider convex sets and functions over idempotent semifields, like the max-plus semifield. We show that if $K$ is a conditionally complete idempotent semifield, with completion $\bar{K}$, a convex function $K^n\to\bar{K}$ which is lower semi-continuous in the order topology is the upper hull of supporting functions defined as residuated differences of affine functions. This result is proved using a separation theorem for closed convex subsets of $K^n$, which extends earlier results of Zimmermann, Samborski, and Shpiz. | |
| dc.description | 25 pages, 4 Postscript figures, v2 (minor revision) | |
| dc.identifier | https://arxiv.org/abs/math/0308166 | |
| dc.identifier | http://arxiv.org/abs/math/0308166 | |
| dc.identifier | Appears in "Idempotent Mathematics and Mathematical Physics", G.L. Litvinov and V.P. Maslov, Eds, vol. 377 of Contemporary Mathematics, pp. 105--129, AMS, 2005. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68335 | |
| dc.subject | Functional Analysis | |
| dc.subject | 26B25 (Primary) 06F20, 06F30 (Secondary) | |
| dc.title | Max-plus convex sets and functions | |
| dc.type | text |