
Journal of Convex Analysis 28 (2021), No. 4, [final page numbers not yet available] 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. 