Intersection Formulae and the Marginal Function in Banach Spaces

Intersection formulae are central to the development of subdifferential calculus and the differentiation of marginal functions. In this paper, we reexamine the connection between independence conditions and intersection formulae. Then we apply the formulae to a general parametric mathematical programming problem in which the constraints are defined by multivalued functions. These results allow us to obtain generalized chain rules for composite functions. Corollaries of this work include several well-known intersection formulae and calculus rules.