Efficient Sample Sizes in Stochastic Nonlinear Programming
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We consider a class of stochastic nonlinear programs for which an approximation to a locally optimal solution is speci_ed in terms of a fractional reduction of the initial cost error. We show that such an approximate solution can be found by approximately solving a sequence of sample average approximations. The key issue in this approach is the determination of the required sequence of sample average approximations as well as the number of iterations to be carried out on each sample average approximation in this sequence. We show that one can express this requirement as an idealized optimization problem whose cost function is the computing work required to obtain the required error reduction. The speci_cation of this idealized optimization problem requires the exact knowledge of a few problems and algorithm parameters. Since the exact values of these parameters are not known, we use estimates, which can be updated as the computation progresses. We illustrate our approach using two numerical examples from structural engineering design.
Journal of Computational and Applied Mathematics, Vol. 217, pp. 301-310.
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