Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral
tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the …

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra
concepts, applications, and computational software packages in an easy-to-use handbook …

We prove that primal-dual log-barrier interior point methods are not strongly polynomial, by
constructing a family of linear programs with 3r+1 inequalities in dimension 2r for which the …

Let be a real closed field with a nontrivial non-archimedean absolute value. We study a
refined version of the tropicalization map, which we call real tropicalization map, that takes …

A polytrope is a tropical polytope which at the same time is convex in the ordinary sense. A d-
dimensional polytrope turns out to be a tropical simplex, that is, it is the tropical convex hull …

We introduce tropical spectrahedra, defined as the images by the nonarchimedean
valuation of spectrahedra over the field of real Puiseux series. We provide an explicit …

We develop a tropical analogue of the simplex algorithm for linear programming. In
particular, we obtain a combinatorial algorithm to perform one tropical pivoting step …

Tropical geometry has been recently used to obtain new complexity results in convex
optimization and game theory. In this paper, we present an application of this approach to a …

This paper is about the combinatorics of finite point configurations in the tropical projective
space or, dually, of arrangements of finitely many tropical hyperplanes. Moreover …

This paper is about the logarithmic limit sets of real semi-algebraic sets, and, more
generally, about the logarithmic limit sets of sets definable in an o-minimal, polynomially …