234 citations · 529 across the 15 of their papers we have counts for
4 papers · 1 filter
The tropical analogue of polar cones
Stéphane Gaubert, Ricardo D. Katz
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…
Cyclic projectors and separation theorems in idempotent convex geometry
Stephane Gaubert, Sergei Sergeev
Semimodules over idempotent semirings like the max-plus or tropical semiring have much in common with convex cones. This analogy is particularly apparent in the case of subsemimodu…
The Minkowski Theorem for Max-plus Convex Sets
Stephane Gaubert, Ricardo Katz
We establish the following max-plus analogue of Minkowski's theorem. Any point of a compact max-plus convex subset of can be written as the max-plus convex c…
The max-plus Martin boundary
Marianne Akian, Stephane Gaubert, Cormac Walsh
We develop an idempotent version of probabilistic potential theory. The goal is to describe the set of max-plus harmonic functions, which give the stationary solutions of determini…