Duality and separation theorems in idempotent semimodules
| dc.creator | Cohen, Guy | |
| dc.creator | Gaubert, Stephane | |
| dc.creator | Quadrat, Jean-Pierre | |
| dc.date | 2002-12-20 | |
| dc.date | 2003-09-29 | |
| dc.date.accessioned | 2026-07-07T04:53:58Z | |
| dc.date.available | 2026-07-07T04:53:58Z | |
| dc.description | We consider subsemimodules and convex subsets of semimodules over semirings with an idempotent addition. We introduce a nonlinear projection on subsemimodules: the projection of a point is the maximal approximation from below of the point in the subsemimodule. We use this projection to separate a point from a convex set. We also show that the projection minimizes the analogue of Hilbert's projective metric. We develop more generally a theory of dual pairs for idempotent semimodules. We obtain as a corollary duality results between the row and column spaces of matrices with entries in idempotent semirings. We illustrate the results by showing polyhedra and half-spaces over the max-plus semiring. | |
| dc.description | 24 pages, 5 Postscript figures, revised (v2) | |
| dc.identifier | https://arxiv.org/abs/math/0212294 | |
| dc.identifier | http://arxiv.org/abs/math/0212294 | |
| dc.identifier | Linear Algebra and its Applications, Volume 379, pages 395--422, March 2004. | |
| dc.identifier | doi:10.1016/j.laa.2003.08.010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66062 | |
| dc.subject | Functional Analysis | |
| dc.subject | Optimization and Control | |
| dc.subject | 46A20 (Primary) 06F07, 46A55 (Secondary) | |
| dc.title | Duality and separation theorems in idempotent semimodules | |
| dc.type | text |