Title Two-stage stochastic linear programming by a series of Monte-Carlo estimators /
Translation of Title Dviejų etapų stochastinis tiesinis programavimas naudojant Monte-Karlo imčių įverčius.
Authors Žilinskas, Kęstutis
DOI 10.15181/csat.v2i2.891
Full Text Download
Is Part of Computational science and techniques.. Klaipėda : Klaipėda University. 2014, Vol. 2, no. 2, p. 289-312.. eISSN 2029-9966
Keywords [eng] Stochastic programming ; Method of Monte-Carlo ; Stochastic gradient ; Statistical criteria ; Epsilon feasible dirction
Abstract [eng] In this paper a stochastic adaptive method has been developed to solve stochastic linear problems by a finite sequence of Monte-Carlo sampling estimators. The method is based on the adaptive regulation of the size of Monte-Carlo samples and a statistical termination procedure taking into consideration statistical modelling accuracy. Our approach distinguishes itself by the treatment of 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. To avoid “jamming” or “zigzagging” solving a constraint problem we implement the ε–feasible direction approach. The proposed adjustment of a sample size, when it is taken inversely proportional to the square of the norm of the Monte-Carlo estimate of the gradient, guarantees convergence a.s. at a linear rate. The numerical study and examples in practice corroborate theoretical conclusions and show that the developed procedures make it possible to solve stochastic problems with sufficient accuracy by the means of an acceptable size of computations.
Published Klaipėda : Klaipėda University
Type Journal article
Language English
Publication date 2014