IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v133y2007i1d10.1007_s10957-007-9178-0.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-007-9178-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-007-9178-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Kurt Marti, 2005. "Stochastic Optimization Methods," Springer Books, Springer, number 978-3-540-26848-2, October.
    3. Sakalauskas, Leonidas L., 2002. "Nonlinear stochastic programming by Monte-Carlo estimators," European Journal of Operational Research, Elsevier, vol. 137(3), pages 558-573, March.
    4. A. Shapiro & Y. Wardi, 1996. "Convergence Analysis of Stochastic Algorithms," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 615-628, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Benjamin Lev, 2005. "Book Reviews," Interfaces, INFORMS, vol. 35(5), pages 436-444, October.
    4. Huiping Yuan & Stephen M. Miller & Langnan Chen, 2011. "The Optimality And Controllability Of Monetary Policy Through Delegation With Consistent Targets," Scottish Journal of Political Economy, Scottish Economic Society, vol. 58(1), pages 82-106, February.
    5. Sun, Haoze & Weng, Chengguo & Zhang, Yi, 2017. "Optimal multivariate quota-share reinsurance: A nonparametric mean-CVaR framework," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 197-214.
    6. Flam, Sjur Didrik & Mirman, Leonard J., 1998. "Groping for optimal growth," Journal of Economic Dynamics and Control, Elsevier, vol. 23(2), pages 191-207, September.
    7. Kenji Hamatani & Masao Fukushima, 2011. "Pricing American options with uncertain volatility through stochastic linear complementarity models," Computational Optimization and Applications, Springer, vol. 50(2), pages 263-286, October.
    8. Wang, Honggang, 2012. "Retrospective optimization of mixed-integer stochastic systems using dynamic simplex linear interpolation," European Journal of Operational Research, Elsevier, vol. 217(1), pages 141-148.
    9. Vladimir Korotin & Arseniy Ulchenkov & Rustam Islamov, 2017. "Debt Portfolio Management for an Oil Company Under Oil Price Uncertainty," Computational Economics, Springer;Society for Computational Economics, vol. 49(2), pages 289-306, February.
    10. Nataša Krejić & Nataša Krklec Jerinkić, 2019. "Spectral projected gradient method for stochastic optimization," Journal of Global Optimization, Springer, vol. 73(1), pages 59-81, January.
    11. Huiping Yuan & Stephen M. Miller, 2006. "The Making of Optimal and Consistent Policy: An Implementation Theory Framework for Monetary Policy," Working papers 2006-06, University of Connecticut, Department of Economics, revised Jan 2009.
    12. 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.
    13. Caroline Geiersbach & Teresa Scarinci, 2021. "Stochastic proximal gradient methods for nonconvex problems in Hilbert spaces," Computational Optimization and Applications, Springer, vol. 78(3), pages 705-740, April.
    14. Huifu Xu & Fanwen Meng, 2007. "Convergence Analysis of Sample Average Approximation Methods for a Class of Stochastic Mathematical Programs with Equality Constraints," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 648-668, August.
    15. Dienstknecht, Michael & Briskorn, Dirk, 2024. "Sharing in construction projects — On determining optimal container assignments for the on-site accommodation of trades," European Journal of Operational Research, Elsevier, vol. 315(1), pages 324-337.
    16. Hachicha, Wafik & Ammeri, Ahmed & Masmoudi, Faouzi & Chachoub, Habib, 2010. "A comprehensive literature classification of simulation optimisation methods," MPRA Paper 27652, University Library of Munich, Germany.
    17. Bartkute, Vaida & Sakalauskas, Leonidas, 2007. "Simultaneous perturbation stochastic approximation of nonsmooth functions," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1174-1188, September.
    18. Liujia Hu & Sigrún Andradóttir, 2019. "An Asymptotically Optimal Set Approach for Simulation Optimization," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 21-39, February.
    19. Lulu He & Jimin Ye & E. Jianwei, 2023. "Accelerated Stochastic Variance Reduction for a Class of Convex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 810-828, March.
    20. Huiping Yuan & Stephen M. Miller & Langnan Chen, 2011. "The Optimality And Controllability Of Monetary Policy Through Delegation With Consistent Targets," Scottish Journal of Political Economy, Scottish Economic Society, vol. 58(1), pages 82-106, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:133:y:2007:i:1:d:10.1007_s10957-007-9178-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.