@article{eprints470,
           title = {Inner and outer approximation of polytopes using boxes},
            year = {2004},
           month = {February},
          volume = {27},
           pages = {151--178},
          number = {2},
       publisher = {Elsevier},
         journal = {Computational Geometry },
          author = {Alberto Bemporad and Carlo Filippi and Fabio Danilo Torrisi},
        keywords = {Polytopes; Approximation; Boxes; Containment; Reachability analysis},
        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.},
             url = {http://eprints.imtlucca.it/470/}
}