Supporting functional
In convex analysis and mathematical optimization, the supporting functional is a generalization of the supporting hyperplane of a set.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.If 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.
