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 …

… Given an H-polytope ♢ : {x: Ax · b} look for two collections ♢ and ♢ of adjacent boxes st: 1.
the union of all boxes in ♢ is contained in ♢ 2. the union of all boxes in ♢ contains ♢
minimize the volume error and minimize the total number of boxes …