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)

## 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 |
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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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