Nonlinear Cone Separation Theorems in Real Reflexive Banach Spaces

The separation of two sets (or more specifically of two cones) plays an important role in different fields of mathematics (e.g. variational analysis, convex analysis, convex geometry, optimization). In this talk, we show some new results for the separation of two (not necessarily convex) cones by a (convex) cone / conical surface in real reflexive Banach spaces. We basically follow the separation approach by Kasimbeyli (2010, SIAM J. Optim. 20), which is based on augmented dual cones and Bishop-Phelps type (nonlinear) separating functions. Classical separation theorems for convex sets are the key tool for proving our main nonlinear cone separation theorems.