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Gradient-based simulation optimization under probability constraints

Author

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  • Andrieu, Laetitia
  • Cohen, Guy
  • Vázquez-Abad, Felisa J.

Abstract

We study optimization problems subject to possible fatal failures. The probability of failure should not exceed a given confidence level. The distribution of the failure event is assumed unknown, but it can be generated via simulation or observation of historical data. Gradient-based simulation-optimization methods pose the difficulty of the estimation of the gradient of the probability constraint under no knowledge of the distribution. In this work we provide two single-path estimators with bias: a convolution method and a finite difference, and we provide a full analysis of convergence of the Arrow-Hurwicz algorithm, which we use as our solver for optimization. Convergence results are used to tune the parameters of the numerical algorithms in order to achieve best convergence rates, and numerical results are included via an example of application in finance.

Suggested Citation

  • Andrieu, Laetitia & Cohen, Guy & Vázquez-Abad, Felisa J., 2011. "Gradient-based simulation optimization under probability constraints," European Journal of Operational Research, Elsevier, vol. 212(2), pages 345-351, July.
    • Handle: RePEc:eee:ejores:v:212:y:2011:i:2:p:345-351
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    Cited by:

    1. Chang, Kuo-Hao, 2015. "A direct search method for unconstrained quantile-based simulation optimization," European Journal of Operational Research, Elsevier, vol. 246(2), pages 487-495.
    2. Chang, Kuo-Hao, 2012. "Stochastic Nelder–Mead simplex method – A new globally convergent direct search method for simulation optimization," European Journal of Operational Research, Elsevier, vol. 220(3), pages 684-694.
    3. Frazier, David T. & Oka, Tatsushi & Zhu, Dan, 2019. "Indirect inference with a non-smooth criterion function," Journal of Econometrics, Elsevier, vol. 212(2), pages 623-645.

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