On the differentiability of the support function

The support function is strongly related to the cost function in economics. Because the differentiability of the cost function is an important property, being related to the celebrated Shephard’s lemma, our propose is to study the differentiability of the support function of a nonempty closed and convex subset of a finite dimensional normed space. So we provide characterizations of the differentiability of the support function on three subsets of its domain. Copyright Springer Science+Business Media, LLC. 2013