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Extensions of Stochastic Optimization Results to Problems with System Failure Probability Functions

Author

Listed:
  • J. O. Royset

    (Naval Postgraduate School)

  • E. Polak

    (University of California)

Abstract

We derive an implementable algorithm for solving nonlinear stochastic optimization problems with failure probability constraints using sample average approximations. The paper extends prior results dealing with a failure probability expressed by a single measure to the case of failure probability expressed in terms of multiple performance measures. We also present a new formula for the failure probability gradient. A numerical example addressing the optimal design of a reinforced concrete highway bridge illustrates the algorithm.

Suggested Citation

  • J. O. Royset & E. Polak, 2007. "Extensions of Stochastic Optimization Results to Problems with System Failure Probability Functions," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 1-18, April.
    • Handle: RePEc:spr:joptap:v:133:y:2007:i:1:d:10.1007_s10957-007-9178-0
    DOI: 10.1007/s10957-007-9178-0
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    References listed on IDEAS

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    1. J. O. Royset & E. Polak, 2004. "Implementable Algorithm for Stochastic Optimization Using Sample Average Approximations," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 157-184, July.
    2. A. Shapiro & Y. Wardi, 1996. "Convergence Analysis of Stochastic Algorithms," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 615-628, August.
    3. Kurt Marti, 2005. "Stochastic Optimization Methods," Springer Books, Springer, number 978-3-540-26848-2, December.
    4. Sakalauskas, Leonidas L., 2002. "Nonlinear stochastic programming by Monte-Carlo estimators," European Journal of Operational Research, Elsevier, vol. 137(3), pages 558-573, March.
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    Cited by:

    1. Johannes Royset, 2013. "On sample size control in sample average approximations for solving smooth stochastic programs," Computational Optimization and Applications, Springer, vol. 55(2), pages 265-309, June.
    2. I. Bremer & R. Henrion & A. Möller, 2015. "Probabilistic constraints via SQP solver: application to a renewable energy management problem," Computational Management Science, Springer, vol. 12(3), pages 435-459, July.
    3. Wim Ackooij & Pedro Pérez-Aros, 2020. "Gradient Formulae for Nonlinear Probabilistic Constraints with Non-convex Quadratic Forms," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 239-269, April.
    4. Byun, Ji-Eun & de Oliveira, Welington & Royset, Johannes O., 2023. "S-BORM: Reliability-based optimization of general systems using buffered optimization and reliability method," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    5. Rockafellar, R.T. & Royset, J.O., 2010. "On buffered failure probability in design and optimization of structures," Reliability Engineering and System Safety, Elsevier, vol. 95(5), pages 499-510.
    6. Lukáš Adam & Martin Branda & Holger Heitsch & René Henrion, 2020. "Solving joint chance constrained problems using regularization and Benders’ decomposition," Annals of Operations Research, Springer, vol. 292(2), pages 683-709, September.

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