Prépublication AOC numéro 03-12

Sur la somme de sous-différentiels de fonctions semi-continues inférieurement
JULES, Florence - Laboratoire A.O.C., Université des Antilles et de la Guyane, Pointe-à-Pitre, F-97159 cedex

The aim of the paper is to present in a unified manner, using an abstract subdifferential and a weaker constraint qualification condition, estimates for the subdifferential of the sum of a finite number of lower semicontinuous functions. With this occasion a comparison of several constraint qualifications is realized. We establish a sum rule involving both an arbitrary subdifferential for the functions in the sum and a subdifferential of Fréchet-type for the sum of the functions. We show that such a rule is actually equivalent to other basic properties of subdifferentials, thus identifying the class of spaces for which it is valid. Specializing the subdifferentials yields refinements of most known strong and weak fuzzy sum rules.