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 the iterative solution of the LP descent direction finding subproblems.