eprintid: 470
rev_number: 10
eprint_status: archive
userid: 7
dir: disk0/00/00/04/70
datestamp: 2011-07-27 08:53:28
lastmod: 2014-07-08 13:58:48
status_changed: 2011-07-27 08:53:28
type: article
metadata_visibility: show
item_issues_count: 0
creators_name: Bemporad, Alberto
creators_name: Filippi, Carlo
creators_name: Torrisi, Fabio Danilo
creators_id: alberto.bemporad@imtlucca.it
creators_id: 
creators_id: 
title: Inner and outer approximation of polytopes using boxes
ispublished: pub
subjects: QA
divisions: CSA
full_text_status: none
keywords: Polytopes; Approximation; Boxes; Containment; Reachability analysis
abstract: 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.
date: 2004-02
date_type: published
publication: Computational Geometry 
volume: 27
number: 2
publisher: Elsevier
pagerange: 151-178
id_number: 10.1016/S0925-7721(03)00048-8
refereed: TRUE
issn: 0925-7721
official_url: http://www.sciencedirect.com/science/article/pii/S0925772103000488
citation:   Bemporad, Alberto and Filippi, Carlo and Torrisi, Fabio Danilo  Inner and outer approximation of polytopes using boxes.  Computational Geometry , 27 (2).  pp. 151-178.  ISSN 0925-7721      (2004)