The Tropical Analogue of Polar Cones
نویسندگان
چکیده
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.
منابع مشابه
On Polar Cones and Differentiability in Reflexive Banach Spaces
Let $X$ be a Banach space, $Csubset X$ be a closed convex set included in a well-based cone $K$, and also let $sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set $C$, so that ${mathop{rm int}}(mathrm{dom} sigma_C) neqem...
متن کاملTropical polar cones, hypergraph transversals, and mean payoff games
We discuss the tropical analogues of several basic questions of convex duality. In particular, the polar of a tropical polyhedral cone represents the set of linear inequalities that its elements satisfy. We characterize the extreme rays of the polar in terms of certain minimal set covers which may be thought of as weighted generalizations of minimal transversals in hypergraphs. We also give a t...
متن کاملPHOSPHOLIPID ANALOGUE DISTRIBUTIONS OF IRANIAN ISOLATES OF CANDIDA
The aim of this study was to analyse polar lipids of Candida species isolated from Ahwaz (Iran) by Fast Atom Bombardment Mass Spectrometry (FAB MS). Nine isolates of Candida Sp. were identified by growth at 45°C, production of chlamydoconidia on cornmeal agar, colonial colour on CHROMagar Candida, germ tube production and ID 32C kits. Then polar lipids were extracted from freeze-dried cult...
متن کاملMinimal external representations of tropical polyhedra
Tropical polyhedra are known to be representable externally, as intersections of finitely many tropical half-spaces. However, unlike in the classical case, the extreme rays of their polar cones provide external representations containing in general superfluous half-spaces. In this paper, we prove that any tropical polyhedral cone in R (also known as “tropical polytope” in the literature) admits...
متن کاملA ug 2 00 9 MINIMAL HALF - SPACES AND EXTERNAL REPRESENTATION OF TROPICAL POLYHEDRA STÉPHANE
We give a characterization of the minimal tropical half-spaces containing a given tropical polyhedron, from which we derive a counter example showing that the number of such minimal half-spaces can be infinite, contradicting some statements which appeared in the tropical literature, and disproving a conjecture of F. Block and J. Yu. We also establish an analogue of the Minkowski-Weyl theorem, s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009