Monte Carlo sampling approach to stochasticprogramming

Various stochastic programming problems can be formulated as problems of optimization of an expected value function. Quite often the corresponding expectation function cannot be computed exactly and should be approximated, say by Monte Carlo sampling methods. In fact, in many practical applications, Monte Carlo simulation is the only reasonable way of estimating the expectation function. We discuss converges properties of the sample average approximation (SAA) approach to stochastic programming. We argue that the SAA method is easily implementable and can be surprisingly efficient for some classes of stochastic programming problems.