Simulation based optimization

In this talk we consider a problem of optimizing an expected value function by Monte Carlo simulation methods. We discuss, somewhat in details, the stochastic counterpart (sample path) method where a relatively large sample is generated and the expected value function is approximated by the corresponding average function. Consequently the obtained approximation problem is solved by deterministic methods of nonlinear programming. One of advantages of this approach, compared with the classical stochastic approximation method, is that a statistical inference can be incorporated into optimization algorithms. This allows to develop a validation analysis, stopping rules and variance reduction techniques which in some cases considerably enhance numerical performance of the stochastic counterpart method.