Directional differentiability of the metric projection in Hilbert space (Q1919883)

The differentiability properties of the metric projection \(P_C\) on a closed convex set \(C\) in Hilbert space are characterized in terms of the smoothness type of the boundary of \(C\). Among others, variational type second-order derivatives (based on variational convergence, i.e., Mosco convergence, Attouch-Wets convergence) of the Minkowski functional \(\mu_C\) at a point \(P_C x\in \partial C\) are used to describe the classical (Gâteaux and Fréchet) first derivative of the operator \(P_C\) at \(x\not\in C\).