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

Author

Listed:
  • B. K. Pagnoncelli

    (Pontifícia Universidade Católica do Rio de Janeiro)

  • S. Ahmed

    (Georgia Institute of Technology)

  • A. Shapiro

    (Georgia Institute of Technology)

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.

Suggested Citation

  • B. K. Pagnoncelli & S. Ahmed & A. Shapiro, 2009. "Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 399-416, August.
    • Handle: RePEc:spr:joptap:v:142:y:2009:i:2:d:10.1007_s10957-009-9523-6
    DOI: 10.1007/s10957-009-9523-6
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