Half-space representation of a closed convex set
= Half-space representation of a closed convex set
A closed <convex set> in a finite-dimensional Euclidean space is the intersection of all containing <closed half-spaces>. For a point outside a nonempty set, its <Euclidean projection onto a convex set> gives a separating normal. Applied to an <epigraph>, this turns geometric separation into affine lower bounds and is a key step in the <Fenchel-Moreau theorem>.