%R 10.1016/S0925-7721(03)00048-8
%N 2
%J Computational Geometry 
%X This paper deals with the problem of approximating a convex polytope in any finite dimension by a collection of (hyper)boxes. More exactly, given a polytope by a system of linear inequalities, we look for two collections and of boxes with non-overlapping interiors such that the union of all boxes in? is contained in? and the union of all boxes in? contains?. We propose and test several techniques to construct and aimed at getting a good balance between two contrasting objectives: minimize the volume error and minimize the total number of generated boxes. We suggest how to modify the proposed techniques in order to approximate the projection of? onto a given subspace without computing the projection explicitly.
%D 2004
%L eprints470
%A Alberto Bemporad
%A Carlo Filippi
%A Fabio Danilo Torrisi
%K Polytopes; Approximation; Boxes; Containment; Reachability analysis
%V 27
%I Elsevier
%T Inner and outer approximation of polytopes using boxes
%P 151-178