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Inner and outer approximation of polytopes using boxes

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)

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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.

Item Type: Article
Identification Number: 10.1016/S0925-7721(03)00048-8
Uncontrolled Keywords: Polytopes; Approximation; Boxes; Containment; Reachability analysis
Subjects: Q Science > QA Mathematics
Research Area: Computer Science and Applications
Depositing User: Professor Alberto Bemporad
Date Deposited: 27 Jul 2011 08:53
Last Modified: 08 Jul 2014 13:58
URI: http://eprints.imtlucca.it/id/eprint/470

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