GRUMMAN AIRCRAFT ENGINEERING CORP BETHPAGE NY RESEARCH DEPT
If f. . . denotes a functional BxM -- E1 B real normed linear space, M metric space, and if fsuperscript o. denotes an associated optimal value functional defined by the rule fsuperscript ox sup f x, mu and the point mu belongs to the set M then the following questions arise 1 Where is fsuperscript o continuous 2 Where is fsuperscript o differentiable. Within the framework of certain reasonable assumptions on the properties of M and f, this paper answers questions 1 and 2. In particular, it offers a necessary and sufficient condition for the existence of a continuous derivative of fsuperscript o on subsets of B.