Directional differentiability of the metric projection in hilbert space

Abstract

The differentiability properties of the metric projection Pc on a closed convex set C in Hilbert space are characterized in terms of the smoothness type of the boundary of C. Our approach is based on using variational type second derivatives as a sufficiently flexible tool to describe the boundary structure of the set C with regard to the differentiability of Pc. We extend results by R.B. Holmes and S. Fitzpatrick and R.R. Phelps. © 1995 by Pacific Journal of Mathematics.