Nonlinear Cone Separation Theorems in Real Topological Linear Spaces

Abstract

The separation of two sets (or more specific of two cones) plays an important role in different fields of mathematics such as variational analysis, convex analysis, convex geometry, optimization. In the paper, we derive some new results for the separation of two not necessarily convex cones by a (convex) cone / conical surface in real (topological) linear spaces. We follow basically the separation approach by Kasimbeyli (2010, SIAM J. Optim. 20) based on augmented dual cones and normlinear separation functions. Classical separation theorems for convex sets will be the key tool for proving our main nonlinear cone separation theorems. Also in the setting of a real reflexive Banach space, we are able to extend the cone separation result derived by Kasimbeyli