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Stochastic Constraints and Variance Reduction Techniques

  • Tito Homem-de-Mello
  • Güzin Bayraksan
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 216)

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work is supported in part by the National Science Foundation under Grant CMMI-1345626, and by Conicyt-Chile under grant Fondecyt 1120244.

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Authors and Affiliations

  1. 1.Universidad Adolfo IbañezSantiagoChile
  2. 2.The Ohio State UniversityColumbusUSA

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