Gradients Généralisés de Fonctions Marginales

Abstract

In this paper, we give different evaluations of generalized gradients of functions defined by: $\varphi _F (x) = {\operatorname{Inf}}\{ {f(x,y)\mid y \in F(x)} \}$. In this expression, f is a locally Lipschitz function on $X \times Y$ and we examine successively the cases: $F(x) = Y$, $F(x) = F$ for all x, and F an arbitrary set-valued mapping with closed graph.