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Article
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 s...
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Chapter
Simulation-Based Optimality Tests for Stochastic Programs
Assessing whether a solution is optimal, or near-optimal, is fundamental in optimization. We describe a simple simulation-based procedure for assessing the quality of a candidate solution to a stochastic progr...
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Article
A probability metrics approach for reducing the bias of optimality gap estimators in two-stage stochastic linear programming
Monte Carlo sampling-based estimators of optimality gaps for stochastic programs are known to be biased. When bias is a prominent factor, estimates of optimality gaps tend to be large on average even for high-...
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Chapter
Stochastic Constraints and Variance Reduction Techniques
We provide an overview of two select topics in Monte Carlo simulation-based methods for stochastic optimization: problems with stochastic constraints and variance reduction techniques. While Monte Carlo simula...
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Article
Variance reduction in Monte Carlo sampling-based optimality gap estimators for two-stage stochastic linear programming
This paper presents a comparative computational study of the variance reduction techniques antithetic variates and Latin hypercube sampling when used for assessing solution quality in stochastic programming. T...
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Article
Identifying effective scenarios in distributionally robust stochastic programs with total variation distance
Traditional stochastic programs assume that the probability distribution of uncertainty is known. However, in practice, the probability distribution oftentimes is not known or cannot be accurately approximated...
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Article
Variance reduction for sequential sampling in stochastic programming
This paper investigates the variance reduction techniques Antithetic Variates (AV) and Latin Hypercube Sampling (LHS) when used for sequential sampling in stochastic programming and presents a comparative comp...
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Article
Residuals-based distributionally robust optimization with covariate information
We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. ...