Variational Analysis in Non-reflexive Spaces and Applications to Control Problems with L1 Perturbations

J. Borwein and Q. J. Zhu

Abstract: We provide a refined sensitivity analysis for finite and infinite horizon control problems where in both cases the perturbation space is $L^1$. Our underlying technique relies on a recent sequential description of both the generalized gradient of Clarke and of the approximate $G$--subdifferential of functions defined on a smooth Banach space. We also show that the proximal limit formula for the generalized gradient and its $L^p$ analogue are direct consequences of these sequential formulas. Related characterizations of Lipschitzness of a function on a smooth space are given.