A Note on Differentiability of Global Optimal Values

The differentiability of global optimal values for smooth constrained programs with respect to general perturbations is considered. The strong Whitney C²-topology is used to the space of objective functions and constraints. It will be shown generically the global optimal value is twice continuously differentiable with respect to the function space of objective functions and constraints. An application of this genericity argument to a nonsmooth objective function—a function of maximum type—is also discussed.