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Inner and Outer Approximations of Polytopes Using Boxes

Author(s):

A. Bemporad, C. Filippi, F.D. Torrisi
Conference/Journal:

vol. AUT02-06
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 $P$ by a system of linear inequalities, we look for two collections $I$ and $E$ of boxes with non-overlapping interiors such that the union of all boxes in $I$ is contained in $P$ and the union of all boxes in $E$ contains $P$. We propose and test several techniques to construct $I$ and $E$ 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 $P$ onto a given subspace without computing the projection explicitly.

Year:

2002
Type of Publication:

(04)Technical Report
Supervisor:



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% Autogenerated BibTeX entry
@TechReport { BemFil:2002:IFA_291,
    author={A. Bemporad and C. Filippi and F.D. Torrisi},
    title={{Inner and Outer Approximations of Polytopes Using Boxes}},
    institution={},
    year={2002},
    number={},
    address={},
    month=dec,
    url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=291}
}
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