Supporting hyperplane is a concept in geometry. A hyperplane divides a space into two half-spaces. A hyperplane is said to support a set S in Euclidean space mathbb R^n if it meets both of the following: S is entirely contained in one of the two closed half-spaces determined by the hyperplane. S has at least one point on the hyperplane.Here, a closed half-space is the half-space that includes the hyperplane.