Frechet differentiability of the metric projection operator in Banach spaces

Abstract

In this paper, we prove Frechet differentiability of the metric projection operator onto closed balls, closed and convex cylinders and positives cones in uniformly convex and uniformly smooth Banach spaces. With respect to these closed and convex subsets, we find the exact expressions for Frechet derivatives and Gateaux directional derivatives of the metric projection operator.