Globally Optimal Parameters

Abstract

In this chapter we study several topics related to global optimality. First we show that one can characterize the parameters that globally optimize the optimal value function on a particular subset of the feasible set called the “region of cooperation”. The characterization is simplified if the so-called “sandwich condition” holds. Optimal parameters can be characterized globally over the entire feasible set, using the classical Lagrangian, if the convex model is LFS. Moreover, for LFS models, neither the region of cooperation nor the sandwich condition is required. These models have another interesting property: One can characterize locally optimal parameters using the classical Lagrangian and without any reference to stability. We also define a “dual” of the convex programming model. This is a finite collection of models each defined over a particular subregion of the feasible set of parameters. In the last section we consider linear programming models having “interval” constraints. Under rather restrictive assumptions, globally optimal parameters of these models can be represented explicitly.