Convergence of Subdifferentials of Convexly Composite Functions

In this paper we establish conditions that guarantee, in the setting of a general Banach space, the Painleve-Kuratowski convergence of the graphs of the subdifferentials of convexly composite functions. We also provide applications to the convergence of multipliers of families of constrained optimization problems and to the generalized second-order derivability of convexly composite functions. Received by the editors March 26, 1998; revised August 5, 1998. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under grant OGP41983 for the second author, and by NATO under grant CRG 960360 for the third author. AMS subject classification: Primary: 49A52, 58C06, 58C20; secondary: 90C30.