Open AccessAPPLICATION OF STATISTICAL CRITERIA TO OPTIMALITY TESTING IN STOCHASTIC PROGRAMMING
Author(s) -
Leonidas Sakalauskas,
Kęstutis Žilinskas
Publication year - 2006
Publication title -
technological and economic development of economy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.634
H-Index - 47
eISSN - 2029-4921
pISSN - 2029-4913
DOI - 10.3846/13928619.2006.9637760
Subject(s) - estimator , monte carlo method , mathematical optimization , rate of convergence , mathematics , sample size determination , statistical hypothesis testing , convergence (economics) , stochastic approximation , constraint (computer aided design) , computation , computer science , algorithm , statistics , computer network , channel (broadcasting) , computer security , key (lock) , economics , economic growth , geometry
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.