
Journal of Convex Analysis 28 (2021), No. 4, 10151032 Copyright Heldermann Verlag 2021 Separating Hyperplanes of Convex Sets Valeriu Soltan Dept. of Mathematical Sciences, George Mason University, Fairfax, VA 22030, U.S.A. vsoltan@gmu.edu [Abstractpdf] Combining existing approaches, we provide a uniform way to describe all hyperplanes which separate (properly, or strong\ly) a given pair of non\emp\ty convex sets $K_1$ and $K_2$ in the $n$dimensional Euclidean space. The method is based on considering $(n\! \! 1)$dimensional subspaces which bound the set $K_1 \!\! K_2$ and then using properties of the polar cone $(K_1 \!\! K_2)^\circ$. First, we characterize all separating hyperplanes with given normal vectors, and then those containing a given point. We also describe the union of all hyperplanes separating (properly separating) a given pair of convex sets. Keywords: Separation, hyperplane, convex, cone. MSC: 52A20, 90C25. [ Fulltextpdf (133 KB)] for subscribers only. 