Journal
SIAM JOURNAL ON OPTIMIZATION
Volume 12, Issue 2, Pages 479-502Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S1052623499363220
Keywords
stochastic programming; discrete optimization; Monte Carlo sampling; law of large numbers; large deviations theory; sample average approximation; stopping rules; stochastic knapsack problem
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In this paper we study a Monte Carlo simulation based approach to stochastic discrete optimization problems. The basic idea of such methods is that a random sample is generated and the expected value function is approximated by the corresponding sample average function. The obtained sample average optimization problem is solved, and the procedure is repeated several times until a stopping criterion is satisfied. We discuss convergence rates, stopping rules, and computational complexity of this procedure and present a numerical example for the stochastic knapsack problem.
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