Mordukhovich Derivatives of Metric Projection Operator in Hilbert Spaces

In this paper, we study the generalized differentiability of the metric projection operator in Hilbert spaces. We find exact expressions for Mordukhovich derivatives (which are also called Mordukhovich coderivatives) for the metric projection operator onto closed balls in Hilbert spaces and positive cones in Euclidean spaces and in real Hilbert space l₂. We investigate the connection between Frèchet derivatives, Gâteaux directional derivatives and the Mordukhovich derivatives of the metric projection in Hilbert spaces.