ON SUBDIFFERENTIALS OF OPTIMAL VALUE-FUNCTIONS

A general mathematical programming problem in which the constraints are defined by multifunctions and depend on a parameter u, and the resulting value function m(u) are considered. In the context of Banach spaces admitting equivalent Frechet differentiable norms estimates for the generalized gradient parital m of m are established. A special study is made of problems in which the multifunctions defining the constraints take convex values. For these problems, estimates for partial m are given in terms of the generalized gradients of the support functions of these multifunctions.