APPLICATION OF THE MONTE-CARLO METHOD TO STOCHASTIC LINEAR PROGRAMMING

L. Sakalauskas and K. Žilinskas
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L. Sakalauskas: Institute of Mathematics and Informatics, Akademijos st 4, 08663 Vilnius, Lithuania
K. Žilinskas: Institute of Mathematics and Informatics, Akademijos st 4, 08663 Vilnius, Lithuania

Chapter 5 in Computer Aided Methods in Optimal Design and Operations, 2006, pp 39-48 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractIn this paper the method by a finite sequence of Monte-Carlo sampling estimators has been developed to solve stochastic linear problems. The method is grounded by 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. To avoid "jamming" or "zigzagging" solving the problem, we implement the ε–feasible direction approach. 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. 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.

Keywords: Optimization; Optimal Design; Global Optimization; Optimal Control (search for similar items in EconPapers)
Date: 2006
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