Variational Analysis in Non-reeexive Spaces and Applications to Control Problems with L 1 Perturbations Please Direct All Correspondence To: Variational Analysis in Non-reeexive Spaces and Applications to Control Problems with L 1 Perturbations

Acknowledgment: We thank Philip D. Loewen for careful and critical reading of an early version of this paper. We also thank Jane J. J. Ye for her comments. Abstract. We provide a reened sensitivity analysis for nite and innnite 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{subdiierential of functions deened 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.