Differentiability of the distance functions

Abstract

            In this paper, we would like to present some findings related to differentiability of the distance functions. These findings have been reported by, Clarke, F. H., Stern R. J., and Wolenski, P. R. However, most of them have not been proved in full details. In this article, they are presented with full details and proofs. 

Keywords: distance function, Hilbert space, Gateaux derivatives, Frechet derivatives, nonsmooth analysis.