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)
Full text not available from this repository.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.
| Item Type: | Article |
|---|---|
| Identification Number: | https://doi.org/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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