Nonlinear stochastic optimization by the Monte-Carlo Method

Methods for solving stochastic optimization problems by Monte-Carlo simulation are considered. The stopping and accuracy of the solutions are treated in a statistical manner, testing the hypothesis of optimality according to statistical criteria. A rule for adjusting the Monte-Carlo sample size is introduced to ensure the convergence and to find the solution of the stochastic optimization problem from an acceptable volume of Monte-Carlo trials. The examples of application of the developed method to importance sampling and the Weber location problem are also considered.