Polyhedral Separability Through Successive LP

We address the problem of discriminating between two finite point sets in the n-dimensional space by h hyperplanes generating a convex polyhedron. If the intersection of the convex hull of 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.