Estimation of Noise-Perturbed Function Values

Abstract

As discussed in the previous two chapters, in stochastic optimization problems some or all of the defining functions (that is, objective and constraints in the model (3.6.1)) depend not only on the decision variables, but also on certain random factors. In such cases the optimization procedure needs to be combined with some—usually time-consuming—function value estimation method, such as experiments or Monte Carlo simulation. Stochastic programming formulations of various engineering or economic design problems (Prékopa, 1980; Ermoliev and Wets, 1988, etc.) may serve as examples of this situation. Obviously, in such cases it is desirable to decrease the number of necessary realizations of the involved random factors as much as possible, while prescribing accuracy and reliability levels (confidence intervals) of the estimated function values: this issue will be addressed below.