Asymptotic analysis of stochastic programs
Annals of Operations Research
Consistent Approximations for Optimal Control Problems Based on Runge--Kutta Integration
SIAM Journal on Control and Optimization
Convergence analysis of stochastic algorithms
Mathematics of Operations Research
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
A branch and bound method for stochastic global optimization
Mathematical Programming: Series A and B
Finding Optimal Material Release Times Using Simulation-Based Optimization
Management Science
Consistent Approximations and Approximate Functions and Gradients in Optimal Control
SIAM Journal on Control and Optimization
Smoothing Method for Minimax Problems
Computational Optimization and Applications
Computational Optimization and Applications
Introduction to Stochastic Search and Optimization
Introduction to Stochastic Search and Optimization
SIAM Journal on Optimization
Variable-sample methods for stochastic optimization
ACM Transactions on Modeling and Computer Simulation (TOMACS)
The Cross Entropy Method: A Unified Approach To Combinatorial Optimization, Monte-carlo Simulation (Information Science and Statistics)
Optimization of Algorithmic Parameters using a Meta-Control Approach*
Journal of Global Optimization
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Efficient sample sizes in stochastic nonlinear programming
Journal of Computational and Applied Mathematics
Variable-Number Sample-Path Optimization
Mathematical Programming: Series A and B
Dynamic Programming and Optimal Control, Vol. II
Dynamic Programming and Optimal Control, Vol. II
The interacting-particle algorithm with dynamic heating and cooling
Journal of Global Optimization
A Model Reference Adaptive Search Method for Global Optimization
Operations Research
Mathematical Programming: Series A and B
Robust Stochastic Approximation Approach to Stochastic Programming
SIAM Journal on Optimization
A Sequential Sampling Procedure for Stochastic Programming
Operations Research
Monte Carlo bounding techniques for determining solution quality in stochastic programs
Operations Research Letters
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We consider smooth stochastic programs and develop a discrete-time optimal-control problem for adaptively selecting sample sizes in a class of algorithms based on variable sample average approximations (VSAA). The control problem aims to minimize the expected computational cost to obtain a near-optimal solution of a stochastic program and is solved approximately using dynamic programming. The optimal-control problem depends on unknown parameters such as rate of convergence, computational cost per iteration, and sampling error. Hence, we implement the approach within a receding-horizon framework where parameters are estimated and the optimal-control problem is solved repeatedly during the calculations of a VSAA algorithm. The resulting sample-size selection policy consistently produces near-optimal solutions in short computing times as compared to other plausible policies in several numerical examples.