46 citations · 71 across the 14 of their papers we have counts for
7 papers · 1 filter
The Geometric Structure of Max-Plus Hemispaces
Daniel Ehrmann, Zach Higgins, Viorel Nitica
Given a set S endowed with a convexity structure, a hemispace is a convex subset of S which has convex complement. We recall that R^n_{max} is a semimodule over the max-plus semifi…
On the dimension of max-min convex sets
Viorel Nitica, Sergei Sergeev
We introduce a notion of dimension of max-min convex sets, following the approach of tropical convexity. We introduce a max-min analogue of the tropical rank of a matrix and show t…
Tropical convexity over max-min semiring
Viorel Nitica, Sergei Sergeev
This is a survey on an analogue of tropical convexity developed over the max-min semiring, starting with the descriptions of max-min segments, semispaces, hyperplanes and an accoun…
Characterization of tropical hemispaces by (P,R)-decompositions
Ricardo D. Katz, Viorel Nitica, Sergei Sergeev
We consider tropical hemispaces, defined as tropically convex sets whose complements are also tropically convex, and tropical semispaces, defined as maximal tropically convex sets…
Best approximation in max-plus semimodules
Marianne Akian, Stephane Gaubert, Viorel Nitica +1
We establish new results concerning projectors on max-plus spaces, as well as separating half-spaces, and derive an explicit formula for the distance in Hilbert's projective metric…
An interval version of separation by semispaces in max-min convexity
Viorel Nitica, Sergei Sergeev
We study separation of a closed box from a max-min convex set by max-min semispace. This can be regarded as an interval extension of known separation results. We give a constructiv…
On hyperplanes and semispaces in max-min convex geometry
Viorel Nitica, Sergei Sergeev
The concept of separation by hyperplanes is fundamental for convex geometry and its tropical (max-plus) analogue. However, analogous separation results in max-min convex geometry a…