3 citations · 8 across the 13 of their papers we have counts for
4 papers · 1 filter
Veronese polytopes: Extending the framework of cyclic polytopes
Marie-Charlotte Brandenburg, Roland Púček
This article introduces the theory of Veronese polytopes, a broad generalisation of cyclic polytopes. These arise as convex hulls of points on curves with one or more connected com…
Decomposition Polyhedra of Piecewise Linear Functions
Marie-Charlotte Brandenburg, Moritz Grillo, Christoph Hertrich
In this paper we contribute to the frequently studied question of how to decompose a continuous piecewise linear (CPWL) function into a difference of two convex CPWL functions. Eve…
The Real Tropical Geometry of Neural Networks
Marie-Charlotte Brandenburg, Georg Loho, Guido Montúfar
We consider a binary classifier defined as the sign of a tropical rational function, that is, as the difference of two convex piecewise linear functions. The parameter space of ReL…
Quotients of M-convex sets and M-convex functions
Marie-Charlotte Brandenburg, Georg Loho, Ben Smith
We unify the study of quotients of matroids, polymatroids, valuated matroids and strong maps of submodular functions in the framework of Murota's discrete convex analysis. As a mai…