Polyhedral Separability through Successive LP

We address the problem of discriminating between two finite point sets, A and B, in the n-dimensional space by h hyperplanes generating a convex polyhedron. If the intersection of the convex hull of A with B is empty, the two sets can be strictly separated (polyhedral separability). We introduce an error function which is piecewise linear but not convex nor concave and define a descent procedure based on iterative solution of LP descent direction finding subproblems.