Stability in generalized differentiability based on a set convergence principle

Abstract

In this paper, we are concerned with epiconvergent sequences of nonsmooth functions. From a general principle of upper set convergence of set-valued maps we derive stability results for various objects in generalized differentiability. In particular, we establish stability results for the Clarke generalized gradient of locally Lipschitz functions, respectively for the generalized Hessian of C 1,1 functions. © 2007 Springer Science + Business Media B.V.