A regularized decomposition method for minimizing a sum of polyhedral functions
Mathematical Programming: Series A and B
Parallel processors for planning under uncertainty
Annals of Operations Research
Statistical verification of optimality conditions for stochastic programs with recourse
Annals of Operations Research
Stochastic decomposition: an algorithm for two-state linear programs with recourse
Mathematics of Operations Research
Annals of Operations Research - Special issue on sensitivity analysis and optimization of discrete event systems
Duality and statistical tests of optimality for two stage stochastic programs
Mathematical Programming: Series A and B
A branch and bound method for stochastic global optimization
Mathematical Programming: Series A and B
A fully sequential procedure for indifference-zone selection in simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Computational Optimization and Applications
Stopping Rules for a Class of Sampling-Based Stochastic Programming Algorithms
Operations Research
Variable-sample methods for stochastic optimization
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Assessing solution quality in stochastic programs
Mathematical Programming: Series A and B
Efficient sample sizes in stochastic nonlinear programming
Journal of Computational and Applied Mathematics
Monte Carlo bounding techniques for determining solution quality in stochastic programs
Operations Research Letters
A Sequential Sampling Procedure for Stochastic Programming
Operations Research
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We develop a sequential sampling procedure for solving a class of stochastic programs. A sequence of feasible solutions, with at least one optimal limit point, is given as input to our procedure. Our procedure estimates the optimality gap of a candidate solution from this sequence, and if that point estimate is sufficiently small then we stop. Otherwise, we repeat with the next candidate solution from the sequence with a larger sample size. We provide conditions under which this procedure: (i) terminates with probability one and (ii) terminates with a solution which has a small optimality gap with a prespecified probability.