Representation of Polytopes as Polynomial Zonotopes
Combinatorics
2019-10-17 v1
Abstract
We prove that each bounded polytope can be represented as a polynomial zonotope, which we refer to as the Z-representation of polytopes. Previous representations are the vertex representation (V-representation) and the halfspace representation (H-representation). Depending on the polytope, the Z-representation can be more compact than the V-representation and the H-representation. In addition, the Z-representation enables the computation of linear maps, Minkowski addition, and convex hull with a computational complexity that is polynomial in the representation size. The usefulness of the new representation is demonstrated by range bounding within polytopes.
Keywords
Cite
@article{arxiv.1910.07271,
title = {Representation of Polytopes as Polynomial Zonotopes},
author = {Niklas Kochdumper and Matthias Althoff},
journal= {arXiv preprint arXiv:1910.07271},
year = {2019}
}