Towards Implementable Nonlinear Stochastic Programming

The concept of implementable nonlinear stochastic programming by finite series of Monte-Carlo samples is surveyed addressing the topics related with stochastic differentiation, stopping rules, conditions of convergence, rational setting of the parameters of algorithms, etc. Our approach distinguishes itself by treatment of the accuracy of solution in a statistical manner, testing the hypothese of optimality according to statistical criteria, and estimating confidence intervals of the objective and constraint functions. The rule for adjusting the Monte-Carlo sample size is introduced which ensures the convergence with the linear rate and enables us to solve the stochastic optimization problem using a reasonable number of Monte-Carlo trials. The issues of implementation of the developed approach in optimal decision making, portfolio optimization, engineering are considered, too.