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.
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.
|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|
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