Application of statistical criteria to optimality testing in stochastic programming - Leonidas Sakalauskas; Kestutis Žilinskas (Technological and Economic Development of Economy, 2006)
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.