relation: http://eprints.imtlucca.it/470/
title: Inner and outer approximation of polytopes using boxes
creator: Bemporad, Alberto
creator: Filippi, Carlo
creator: Torrisi, Fabio Danilo
subject: QA Mathematics
description: 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.
publisher: Elsevier
date: 2004-02
type: Article
type: PeerReviewed
identifier:   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)  
relation: http://www.sciencedirect.com/science/article/pii/S0925772103000488
relation: 10.1016/S0925-7721(03)00048-8