IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v85y1999i0p1-1910.1023-a1018909508556.html
   My bibliography  Save this article

Duality and optimality in multistagestochastic programming

Author

Listed:
  • R.T. Rockafellar

Abstract

A model of multistage stochastic programming over a scenario tree is developed, in whichthe evolution of information states, as represented by the nodes of a scenario tree, is supplementedby a dynamical system of state vectors controlled by recourse decisions. A dualproblem is obtained in which multipliers associated with the primal dynamics are pricevectors that are propagated backward in time through a dual dynamical system involvingconditional expectation. A format of Fenchel duality is employed in order to have immediatespecialization not only to linear programming but also to extended linear‐quadratic programming.The resulting optimality conditions support schemes of decomposition in which aseparate optimization problem is solved at each node of the scenario tree. Copyright Kluwer Academic Publishers 1999

Suggested Citation

  • R.T. Rockafellar, 1999. "Duality and optimality in multistagestochastic programming," Annals of Operations Research, Springer, vol. 85(0), pages 1-19, January.
    • Handle: RePEc:spr:annopr:v:85:y:1999:i:0:p:1-19:10.1023/a:1018909508556
    DOI: 10.1023/A:1018909508556
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/A:1018909508556
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1023/A:1018909508556?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.

    Citations

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


    Cited by:

    1. Guigues, Vincent & Shapiro, Alexander & Cheng, Yi, 2023. "Duality and sensitivity analysis of multistage linear stochastic programs," European Journal of Operational Research, Elsevier, vol. 308(2), pages 752-767.
    2. Alain Carpentier & Alexandre Gohin, 2015. "On the economic theory of crop rotations: value of the crop rotation effects and implications on acreage choice modeling," Working Papers SMART 15-04, INRAE UMR SMART.
    3. Qingjie Hu & Jiguang Wang & Yu Chen, 2020. "New dualities for mathematical programs with vanishing constraints," Annals of Operations Research, Springer, vol. 287(1), pages 233-255, April.
    4. Michael S. Casey & Suvrajeet Sen, 2005. "The Scenario Generation Algorithm for Multistage Stochastic Linear Programming," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 615-631, August.
    5. Pedro Borges, 2022. "Cut-sharing across trees and efficient sequential sampling for SDDP with uncertainty in the RHS," Computational Optimization and Applications, Springer, vol. 82(3), pages 617-647, July.
    6. S. K. Mishra & Vinay Singh & Vivek Laha, 2016. "On duality for mathematical programs with vanishing constraints," Annals of Operations Research, Springer, vol. 243(1), pages 249-272, August.
    7. Diana Barro & Elio Canestrelli, 2016. "Combining stochastic programming and optimal control to decompose multistage stochastic optimization problems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(3), pages 711-742, July.

    More about this item

    Statistics

    Access and download statistics

    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:85:y:1999:i:0:p:1-19:10.1023/a:1018909508556. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.