Asymptotic analysis of stochastic programs
Annals of Operations Research
Stochastic decomposition: an algorithm for two-state linear programs with recourse
Mathematics of Operations Research
Sample-path optimization of convex stochastic performance functions
Mathematical Programming: Series A and B
Analysis of sample-path optimization
Mathematics of Operations Research
Retrospective simulation response optimization
WSC '91 Proceedings of the 23rd conference on Winter simulation
Finding Optimal Material Release Times Using Simulation-Based Optimization
Management Science
The Sample Average Approximation Method for Stochastic Discrete Optimization
SIAM Journal on Optimization
Computational Optimization and Applications
Feature Article: Optimization for simulation: Theory vs. Practice
INFORMS Journal on Computing
Introduction to Stochastic Search and Optimization
Introduction to Stochastic Search and Optimization
Variable-sample methods for stochastic optimization
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Convex Optimization
Assessing solution quality in stochastic programs
Mathematical Programming: Series A and B
Convergence theory for nonconvex stochastic programming with an application to mixed logit
Mathematical Programming: Series A and B
On choosing parameters in retrospective-approximation algorithms for simulation-optimization
Proceedings of the 38th conference on Winter simulation
Convex Approximations of Chance Constrained Programs
SIAM Journal on Optimization
Efficient sample sizes in stochastic nonlinear programming
Journal of Computational and Applied Mathematics
Retrospective-approximation algorithms for the multidimensional stochastic root-finding problem
ACM Transactions on Modeling and Computer Simulation (TOMACS)
A Sequential Sampling Procedure for Stochastic Programming
Operations Research
Monte Carlo bounding techniques for determining solution quality in stochastic programs
Operations Research Letters
The mathematics of continuous-variable simulation optimization
Proceedings of the 40th Conference on Winter Simulation
The stochastic root-finding problem: Overview, solutions, and open questions
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Proceedings of the Winter Simulation Conference
An introspective on the retrospective-approximation paradigm
Proceedings of the Winter Simulation Conference
Proceedings of the Winter Simulation Conference
Convergence properties of direct search methods for stochastic optimization
Proceedings of the Winter Simulation Conference
Root finding via darts: dynamic adaptive random target shooting
Proceedings of the Winter Simulation Conference
Line search methods with variable sample size for unconstrained optimization
Journal of Computational and Applied Mathematics
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On sample size control in sample average approximations for solving smooth stochastic programs
Computational Optimization and Applications
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The stochastic root-finding problem is that of finding a zero of a vector-valued function known only through a stochastic simulation. The simulation-optimization problem is that of locating a real-valued function's minimum, again with only a stochastic simulation that generates function estimates. Retrospective approximation (RA) is a sample-path technique for solving such problems, where the solution to the underlying problem is approached via solutions to a sequence of approximate deterministic problems, each of which is generated using a specified sample size, and solved to a specified error tolerance. Our primary focus, in this paper, is providing guidance on choosing the sequence of sample sizes and error tolerances in RA algorithms. We first present an overview of the conditions that guarantee the correct convergence of RA's iterates. Then we characterize a class of error-tolerance and sample-size sequences that are superior to others in a certain precisely defined sense. We also identify and recommend members of this class and provide a numerical example illustrating the key results.