WSC '04 Proceedings of the 36th conference on Winter simulation
Gradient-based simulation optimization
Proceedings of the 38th conference on Winter simulation
Non-linear control variates for regenerative steady-state simulation
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Comparing two systems: beyond common random numbers
Proceedings of the 40th Conference on Winter Simulation
A Sequential Sampling Procedure for Stochastic Programming
Operations Research
Line search methods with variable sample size for unconstrained optimization
Journal of Computational and Applied Mathematics
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Monte Carlo methods have extensively been used and studied in the area of stochastic programming. Their convergence properties typically consider global minimizers or first-order critical points of the sample average approximation (SAA) problems and minimizers of the true problem, and show that the former converge to the latter for increasing sample size. However, the assumption of global minimization essentially restricts the scope of these results to convex problems. We review and extend these results in two directions: we allow for local SAA minimizers of possibly nonconvex problems and prove, under suitable conditions, almost sure convergence of local second-order solutions of the SAA problem to second-order critical points of the true problem. We also apply this new theory to the estimation of mixed logit models for discrete choice analysis. New useful convergence properties are derived in this context, both for the constrained and unconstrained cases, and associated estimates of the simulation bias and variance are proposed.