Asymptotic behavior of empirical estimators in stochastic programming problems

In the solution of stochastic optimization and estimation problems it is not always possible to find the exact value of the optimum of the mathematical expectation of a random function. Therefore, instead of the original criterion function it is proposed to consider an empirical estimator of it, for which the optimization problem is solved. Conditions are found for the optimum points of the empirical criterion function to converge in a certain probabilistic sense to an optimum point of the original problem.