Nonlinear stochastic programming by Monte-Carlo estimators

Methods for solving stochastic programming (SP) problems by a finite series of Monte-Carlo samples are considered. The accuracy of solution is treated in a statistical manner, testing the hypothesis of optimality according to statistical criteria. The rule for adjusting the Monte-Carlo sample size is introduced to ensure the convergence and to find the solution of the SP problem using a reasonable number of Monte-Carlo trials. Issues of implementation of the developed approach in decision making and other applicable fields are considered too.