Convergence of subdifferentials of convexly composite functions

In this paper we establish conditions that guarantee, in the setting of a g eneral Banach space, the Painleve-Kuratowski convergence of the graphs of t he subdifferentials of convexly composite functions. We also provide applic ations to the convergence of multipliers of families of constrained optimiz ation problems and to the generalized second-order derivability of convexly composite functions.