Stochastic Constraints and Variance Reduction Techniques

Tito Homem- de-Mello () and Güzin Bayraksan ()
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Tito Homem- de-Mello: Universidad Adolfo Ibañez
Güzin Bayraksan: The Ohio State University

Chapter Chapter 9 in Handbook of Simulation Optimization, 2015, pp 245-276 from Springer

Abstract: Abstract 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 simulation-based methods have been successfully used for stochastic optimization problems with deterministic constraints, there is a growing body of work on its use for problems with stochastic constraints. The presence of stochastic constraints brings new challenges in ensuring and testing optimality, allocating sample sizes, etc., especially due to difficulties in determining feasibility. We review results for general stochastic constraints and also discuss special cases such as probabilistic and stochastic dominance constraints. Next, we review the use of variance reduction techniques (VRT) in a stochastic optimization setting. While this is a well-studied topic in statistics and simulation, the use of VRT in stochastic optimization requires a more thorough analysis. We discuss asymptotic properties of the resulting approximations and their use within Monte Carlo simulation-based solution methods.

Keywords: Importance Sampling; Stochastic Optimization; Latin Hypercube Sampling; Stochastic Optimization Problem; Variance Reduction Technique (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-1-4939-1384-8_9

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