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Journal of Optimization Theory and Applications

, Volume 142, Issue 2, pp 399–416 | Cite as

Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications

  • B. K. Pagnoncelli
  • S. Ahmed
  • A. Shapiro
Article

Abstract

We study sample approximations of chance constrained problems. In particular, we consider the sample average approximation (SAA) approach and discuss the convergence properties of the resulting problem. We discuss how one can use the SAA method to obtain good candidate solutions for chance constrained problems. Numerical experiments are performed to correctly tune the parameters involved in the SAA. In addition, we present a method for constructing statistical lower bounds for the optimal value of the considered problem and discuss how one should tune the underlying parameters. We apply the SAA to two chance constrained problems. The first is a linear portfolio selection problem with returns following a multivariate lognormal distribution. The second is a joint chance constrained version of a simple blending problem.

Keywords

Chance constraints Sample average approximation Portfolio selection 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Departamento de MatemáticaPontifícia Universidade Católica do Rio de JaneiroRio de JaneiroBrazil
  2. 2.Georgia Institute of TechnologyAtlantaUSA

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