%0 Journal Article
%@ 0925-7721
%A Bemporad, Alberto
%A Filippi, Carlo
%A Torrisi, Fabio Danilo
%D 2004
%F eprints:470
%I Elsevier
%J Computational Geometry 
%K Polytopes; Approximation; Boxes; Containment; Reachability analysis
%N 2
%P 151-178
%T Inner and outer approximation of polytopes using boxes
%U http://eprints.imtlucca.it/470/
%V 27
%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.