In convex analysis and mathematical optimization, the supporting functional is a generalization of the supporting hyperplane of a set. Mathematical definition Let X be a locally convex topological space, and be a convex set, then the continuous linear functional is a supporting functional of C at the point if and for every . Relation to support function If (where is the dual space of ) is a support function of the set C, then if , it follows that defines a supporting functional of C at the point such that for any . Relation to supporting hyperplane If is a supporting functional of the convex set C at the point such that then defines a supporting hyperplane to C at . References Functional analysis Duality theories Types of functions