HIGH-ORDER POINT VARIATIONS AND GENERALIZED DIFFERENTIALS
H�ctor J. Sussmann · Series on advances in mathematics for applied sciences · 2008
www.math.rutgers.edu / �sussmann In a series of nonsmooth versions of the Pontryagin Maximum Principle, we used generalized differentials of set-valued maps, flows, and abstract variations. Bianchini and Stefani have introduced a notion of possibly high-order variational vector that has the summability property. We consider a slightly more general class of variational vectors than that defined by Bianchini and Stefani, and prove that the convex combinations of these vectors arise as “differentials ” of variations that are differentiable in the sense of one of our generalized differentiation theories, namely, that of “approximate generalized differential quotients ” (AGDQs). 1.