TY  - JOUR
VL  - 27
PB  - Elsevier
A1  - Bemporad, Alberto
A1  - Filippi, Carlo
A1  - Torrisi, Fabio Danilo
SP  - 151
Y1  - 2004/02//
JF  - Computational Geometry 
IS  - 2
ID  - eprints470
EP  - 178
SN  - 0925-7721
N2  - 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.
KW  - Polytopes; Approximation; Boxes; Containment; Reachability analysis
AV  - none
TI  - Inner and outer approximation of polytopes using boxes
UR  - http://www.sciencedirect.com/science/article/pii/S0925772103000488
ER  -