Optimal Value Function

Abstract

The optimal value function of a convex model generally is not continuous and it is not known analytically. Still, in some situations, it is possible to obtain enough information about it in order to calculate and describe its local and global optima. The main objective of this chapter is to obtain formulas for the “directional derivative” of the optimal value function relative to a prescribed stable path. These formulas can be used to improve the value of the function at some given parameter and, when applied iteratively, to formulate input optimization methods. We will use these methods to solve two real-life problems. Optimality of the parameters can be verified ( at least in principle), by some of the results proved in the preceding sections. A list of necessary conditions for local or global optimality of a parameter is compiled at the end of the chapter.