97 citations · 431 across the 34 of their papers we have counts for
9 papers · 1 filter
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…
Tropical linear-fractional programming and parametric mean payoff games
Stephane Gaubert, Ricardo D. Katz, Sergei Sergeev
Tropical polyhedra have been recently used to represent disjunctive invariants in static analysis. To handle larger instances, tropical analogues of classical linear programming re…
The level set method for the two-sided eigenproblem
Stephane Gaubert, Sergei Sergeev
We consider the max-plus analogue of the eigenproblem for matrix pencils Ax=lambda Bx. We show that the spectrum of (A,B) (i.e., the set of possible values of lambda), which is a f…
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…
On visualisation scaling, subeigenvectors and Kleene stars in max algebra
Sergei Sergeev, Hans Schneider, Peter Butkovic
The purpose of this paper is to investigate the interplay arising between max algebra, convexity and scaling problems. The latter, which have been studied in nonnegative matrix the…
Multiorder, Kleene stars and cyclic projectors in the geometry of max cones
Sergei Sergeev
This paper summarizes results on some topics in the max-plus convex geometry, mainly concerning the role of multiorder, Kleene stars and cyclic projectors, and relates them to some…
Max-plus definite matrix closures and their eigenspaces
Sergei Sergeev
In this paper we introduce the definite closure operation for max-plus matrices with finite permanent, reveal inner structures of definite eigenspaces, and establish some facts abo…