The tropical analogue of polar cones

被引：17
|
作者：
Gaubert, Stephane [2 ,3 ]
Katz, Ricardo D. [1 ]
机构：
[1] Univ Nacl Rosario, CONICET, Inst Matemat Beppo Levi, RA-2000 Rosario, Santa Fe, Argentina
[2] Ecole Polytech, INRIA, F-91128 Palaiseau, France
[3] Ecole Polytech, Ctr Math Appl, F-91128 Palaiseau, France
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2009年 / 431卷 / 5-7期
关键词：
Max-plus semiring; Max-plus convexity; Tropical convexity; Extremal convexity; B-convexity; Duality; Separation theorem; Farkas lemma; Semimodules; Idempotent spaces; PLUS CONVEX-SETS; MAX; SEPARATION; THEOREM; SYSTEM;
D O I：
10.1016/j.laa.2009.03.012
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the max-plus or tropical analogue of the notion of polar: the polar of a cone represents the set of linear inequalities satisfied by its elements. We establish an analogue of the bipolar theorem, which characterizes all the inequalities satisfied by the elements of a tropical convex cone. We derive this characterization from a new separation theorem. We also establish variants of these results concerning systems of linear equalities. (c) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码：608 / 625
页数：18
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