DIRECTIONAL DIFFERENTIABILITY OF THE METRIC PROJECTION IN HILBERT-SPACE

The differentiability properties of the metric projection Pc on a clos ed convex set C in Hilbert space are characterized in terms of the smo othness type of the boundary of C. Our approach is based on using vari ational type second derivatives as a sufficiently flexible tool to des cribe the boundary structure of the set C with regard to the different iability of Pc. We extend results by R.B. Holmes and S. Fitzpatrick an d R.R. Phelps.