Assessing solution quality in stochastic programs
نویسندگان
چکیده
منابع مشابه
Assessing Solution Quality in Stochastic Programs
Determining whether a solution is of high quality (optimal or near optimal) is fundamental in optimization theory and algorithms. In this paper, we develop Monte Carlo sampling-based procedures for assessing solution quality in stochastic programs. Quality is defined via the optimality gap and our procedures’ output is a confidence interval on this gap. We review a multiple-replications procedu...
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Determining if a solution is optimal or near optimal is fundamental in optimization theory, algorithms, and computation. For instance, Karush-Kuhn-Tucker conditions provide necessary and sufficient optimality conditions for certain classes of problems, and bounds on optimality gaps are frequently used as part of optimization algorithms. Such bounds are obtained through Lagrangian, integrality, ...
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Determining whether a solution is of high quality (optimal or near optimal) is a fundamental question in optimization theory and algorithms. We develop a Monte Carlo sampling-based procedure for assessing solution quality in stochastic programs. Quality is defined via the optimality gap and our procedure’s output is a confidence interval on this gap. We present a result that justifies a single-...
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A stochastic program SP with solution value z∗ can be approximately solved by sampling n realizations of the program’s stochastic parameters, and by solving the resulting “approximating problem” for (x∗ n ; z ∗ n ). We show that, in expectation, z ∗ n is a lower bound on z∗ and that this bound monotonically improves as n increases. The rst result is used to construct con dence intervals on the ...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2006
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-006-0720-x