Conjugate of the squared distance to a convex set ($d_C^{\ast }(p)=\frac{1}{2}\Vert p{\Vert }^2+{\sigma }_C(p)$)

The squared distance to a convex set is the infimal convolution of the set's indicator functional of a constraint set and the half-squared Hilbert space norm. Its convex conjugate is the sum of the half-squared norm and the support function of the set.