Separation of convex sets by Clarke subdifferential

Abstract

In this article we consider a separation technique proposed in J. Grzybowski, D. Pallaschke, and R. Urbański (A pre-classification and the separation law for closed bounded convex sets, Optim. Method Softw. 20(2005), pp. 219–229) for separating two convex sets A and B with another convex set C. We prove that in a finite dimension C can be chosen as the Clarke subdifferential at the origin of , where pA , pB denotes the support functions of A and B respectively.