A Sequential Sampling Procedure for Stochastic Programming

Güzi̇n Bayraksan · David P. Morton

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Risk and Portfolio Optimization Advanced Optimization Algorithms Research Simulation Techniques and Applications

Abstract

We develop a sequential sampling procedure for a class of stochastic programs. We assume that a sequence of feasible solutions with an optimal limit point is given as input to our procedure. Such a sequence can be generated by solving a series of sampling problems with increasing sample size, or it can be found by any other viable method. Our procedure estimates the optimality gap of a candidate solution from this sequence. If the point estimate of the optimality gap is sufficiently small according to our termination criterion, then we stop. Otherwise, we repeat with the next candidate solution from the sequence under an increased sample size. We provide conditions under which this procedure (i) terminates with probability one and (ii) terminates with a solution that has a small optimality gap with a prespecified probability.

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References

1983Simulation Modeling and Analysis.2011Introduction to Stochastic Programming 2002The Sample Average Approximation Method for Stochastic Discrete Optimization 2003Monte Carlo Sampling Methods 1999Monte Carlo bounding techniques for determining solution quality in stochastic programs 1988Numerical Techniques for Stochastic Optimization 2006The empirical behavior of sampling methods for stochastic programming 2001A fully sequential procedure for indifference-zone selection in simulation

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