Calmness and exact penalization
SIAM Journal on Control and Optimization
Asymptotic theory for solutions in statistical estimation and stochastic programming
Mathematics of Operations Research
Sample-path optimization of convex stochastic performance functions
Mathematical Programming: Series A and B
Optimization: algorithms and consistent approximations
Optimization: algorithms and consistent approximations
A simulation-based approach to two-stage stochastic programming with recourse
Mathematical Programming: Series A and B
Sequential sampling for solving stochastic programs
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
The mathematics of continuous-variable simulation optimization
Proceedings of the 40th Conference on Winter Simulation
A Sequential Sampling Procedure for Stochastic Programming
Operations Research
An introspective on the retrospective-approximation paradigm
Proceedings of the Winter Simulation Conference
Line search methods with variable sample size for unconstrained optimization
Journal of Computational and Applied Mathematics
On sample size control in sample average approximations for solving smooth stochastic programs
Computational Optimization and Applications
Hi-index | 7.30 |
We consider a class of stochastic nonlinear programs for which an approximation to a locally optimal solution is specified 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 specification 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.