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.