El método de aproximación por media muestral

Abstract

The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. The basic idea of such method is that we can approximate the expected objetive function by the corresponding sample average function using a random sample. We solve the obtained sample average approximating problem by deterministic optimization techniques, and the process is repeated several times with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps until a stopping criterion is satisfied. In section 1 we describe the expected value and sample average approximation problems and give a few examples of real cases in which it can be useful. In section 2 we show many results related to convergence of estimators (objective value, optimal solution, etc) under certain assumptions. In section 3 we discuss convergence rates of objetive values. In section 4 we implement the method to study two problems (that involve different random variables) to illustrate the power of the method.