On Subdifferentials of Optimal Value Functions
Lionel Thibault · SIAM Journal on Control and Optimization · 1991
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 Fréchet differentiable norms estimates for the generalized gradient $\partial m$ 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.