APPLICATION OF STATISTICAL CRITERIA TO OPTIMALITY TESTING IN STOCHASTIC PROGRAMMING
提出一种自适应随机方法，通过蒙特卡洛样本和统计终止准则求解随机线性问题，检验最优性假设并估计置信区间，数值实验验证了方法的有效性。
In this paper the stochastic adaptive method has been developed to solve stochastic linear problems by a finite sequence of Monte‐Carlo sampling estimators. The method is grounded on adaptive regulation of the size of Monte‐Carlo samples and the statistical termination procedure, taking into consideration the statistical modeling error. Our approach distinguishes itself by treatment of the accuracy of the solution in a statistical manner, testing the hypothesis of optimality according to statistical criteria, and estimating confidence intervals of the objective and constraint functions. The adjustment of sample size, when it is taken inversely proportional to the square of the norm of the Monte‐Carlo estimate of the gradient, guarantees the convergence a. s. at a linear rate. We examine four estimators for stochastic gradient: by the differentiation of the integral with respect to x, the finite difference approach, the Simulated Perturbation Stochastic Approximation approach, the Likelihood Ratio approach. The numerical study and examples in practice corroborate the theoretical conclusions and show that the procedures developed make it possible to solve stochastic problems with a sufficient agreeable accuracy by means of the acceptable amount of computations.