IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v165y2009i1p29-4510.1007-s10479-008-0355-9.html
   My bibliography  Save this article

The Expected loss in the discretization of multistage stochastic programming problems—estimation and convergence rate

Author

Listed:
  • Martin Šmíd

Abstract

In the present paper, the approximate computation of a multistage stochastic programming problem (MSSPP) is studied. First, the MSSPP and its discretization are defined. Second, the expected loss caused by the usage of the “approximate” solution instead of the “exact” one is studied. Third, new results concerning approximate computation of expectations are presented. Finally, the main results of the paper—an upper bound of the expected loss and an estimate of the convergence rate of the expected loss—are stated. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • Martin Šmíd, 2009. "The Expected loss in the discretization of multistage stochastic programming problems—estimation and convergence rate," Annals of Operations Research, Springer, vol. 165(1), pages 29-45, January.
    • Handle: RePEc:spr:annopr:v:165:y:2009:i:1:p:29-45:10.1007/s10479-008-0355-9
    DOI: 10.1007/s10479-008-0355-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-008-0355-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-008-0355-9?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. Teemu Pennanen, 2005. "Epi-Convergent Discretizations of Multistage Stochastic Programs," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 245-256, February.
    Full references (including those not matched with items on IDEAS)

    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. D. Kuhn, 2009. "Convergent Bounds for Stochastic Programs with Expected Value Constraints," Journal of Optimization Theory and Applications, Springer, vol. 141(3), pages 597-618, June.
    2. Michael Chen & Sanjay Mehrotra & Dávid Papp, 2015. "Scenario generation for stochastic optimization problems via the sparse grid method," Computational Optimization and Applications, Springer, vol. 62(3), pages 669-692, December.
    3. Boris Defourny & Damien Ernst & Louis Wehenkel, 2013. "Scenario Trees and Policy Selection for Multistage Stochastic Programming Using Machine Learning," INFORMS Journal on Computing, INFORMS, vol. 25(3), pages 488-501, August.
    4. Julien Keutchayan & Michel Gendreau & Antoine Saucier, 2017. "Quality evaluation of scenario-tree generation methods for solving stochastic programming problems," Computational Management Science, Springer, vol. 14(3), pages 333-365, July.
    5. Rocha, Paula & Kuhn, Daniel, 2012. "Multistage stochastic portfolio optimisation in deregulated electricity markets using linear decision rules," European Journal of Operational Research, Elsevier, vol. 216(2), pages 397-408.
    6. Raffaello Seri & Christine Choirat, 2013. "Scenario Approximation of Robust and Chance-Constrained Programs," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 590-614, August.
    7. Gah-Yi Ban & Jérémie Gallien & Adam J. Mersereau, 2019. "Dynamic Procurement of New Products with Covariate Information: The Residual Tree Method," Manufacturing & Service Operations Management, INFORMS, vol. 21(4), pages 798-815, October.
    8. Huynh Thi Hong Diem, 2022. "Consistency of statistical estimators of solutions to stochastic optimization problems," Journal of Global Optimization, Springer, vol. 83(4), pages 825-842, August.
    9. Tahir Ekin & Nicholas G. Polson & Refik Soyer, 2014. "Augmented Markov Chain Monte Carlo Simulation for Two-Stage Stochastic Programs with Recourse," Decision Analysis, INFORMS, vol. 11(4), pages 250-264, December.

    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:annopr:v:165:y:2009:i:1:p:29-45:10.1007/s10479-008-0355-9. 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.