Polyhedral Separability Through Successive LP

We address the problem of discriminating between two finite point sets $$\mathcal{A}{\text{ and }}\mathcal{B}$$ in the n-dimensional space by h hyperplanes generating a convex polyhedron. If the intersection of the convex hull of $$\mathcal{A}{\text{ with }}\mathcal{B}$$ 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.