SOME RESULTS ON SECOND ORDER DIFFERENTIABILITY IN THE EXTENDED SENSE OF FUNCTIONS

Abstract

In this paper, we introduce the concept of second order partial derivatives in the extended sense for nonconvex functions and prove a formula computing the extended Hessian in terms of the second order partial derivatives in the extended sense. We show that the sum, difference, product, and quotient of functions that are twice differentiable at a point are functions that are twice differentiable at that point in the extended sense. We also show why the counterpart of the second order differentiability in the extended sense on Rn does not appear in variational analysis.