The empirical behavior of sampling methods for stochastic programming |
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| Authors: | Jeff Linderoth Alexander Shapiro Stephen Wright |
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| Affiliation: | (1) Industrial and Systems Engineering Department, Lehigh University, 200 West Packer Avenue, Bethlehem, PA, 18015;(2) School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332;(3) Computer Sciences Department, University of Wisconsin-Madison, 1210 West Dayton Street, Madison, WI, 53706 |
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| Abstract: | We investigate the quality of solutions obtained from sample-average approximations to two-stage stochastic linear programs with recourse. We use a recently developed software tool executing on a computational grid to solve many large instances of these problems, allowing us to obtain high-quality solutions and to verify optimality and near-optimality of the computed solutions in various ways. Research supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under Contract W-31-109-Eng-38, and by the National Science Foundation under Grant 9726385. Research supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under Contract W-31-109-Eng-38, and by the National Science Foundation under Grant DMS-0073770. Research supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under Contract W-31-109-Eng-38, and by the National Science Foundation under Grants 9726385 and 0082065. |
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| Keywords: | Stochastic linear programming Recourse Sample average approximations Computational grid Monte Carlo sampling Optimality gap Statistical KKT test |
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