Stochastic constraints and variance reduction techniques

Tito Homem-De-Mello, Güzin Bayraksan

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

7 Scopus citations

Abstract

We provide an overview of two select topics in Monte Carlo simulationbased 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.

Original languageEnglish
Title of host publicationInternational Series in Operations Research and Management Science
PublisherSpringer New York LLC
Pages245-276
Number of pages32
DOIs
StatePublished - 2015
Externally publishedYes

Publication series

NameInternational Series in Operations Research and Management Science
Volume216
ISSN (Print)0884-8289

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