Name
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 | DOI | Venue |
|---|---|---|
2004 | 10.1016/S0925-7721(03)00048-8 | Comput. Geom. |
Keywords | Field | DocType |
linear inequality,polytope p,total number,paper deal,outer approximation,polytopes,good balance,boxes,volume error,convex polytope,proposed technique,approximation,containment,non-overlapping interior,finite dimension,reachability analysis | Discrete mathematics,Combinatorics,Subspace topology,Approximations of π,Convex polytope,Polytope,Linear inequality,Mathematics | Journal |
Volume | Issue | ISSN |
27 | 2 | Computational Geometry: Theory and Applications |
Citations | PageRank | References |
24 | 1.57 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alberto Bemporad | 1 | 4353 | 568.62 |
| Carlo Filippi | 2 | 168 | 13.77 |
| Fabio D. Torrisi | 3 | 87 | 15.91 |