IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v142y2006i1p129-14610.1007-s10479-006-6165-z.html
   My bibliography  Save this article

Multistage stochastic convex programs: Duality and its implications

Author

Listed:
  • Julia Higle
  • Suvrajeet Sen

Abstract

In this paper, we study alternative primal and dual formulations of multistage stochastic convex programs (SP). The alternative dual problems which can be traced to the alternative primal representations, lead to stochastic analogs of standard deterministic constructs such as conjugate functions and Lagrangians. One of the by-products of this approach is that the development does not depend on dynamic programming (DP) type recursive arguments, and is therefore applicable to problems in which the objective function is non-separable (in the DP sense). Moreover, the treatment allows us to handle both continuous and discrete random variables with equal ease. We also investigate properties of the expected value of perfect information (EVPI) within the context of SP, and the connection between EVPI and nonanticipativity of optimal multipliers. Our study reveals that there exist optimal multipliers that are nonanticipative if, and only if, the EVPI is zero. Finally, we provide interpretations of the retroactive nature of the dual multipliers. Copyright Springer Science + Business Media, Inc. 2006

Suggested Citation

  • Julia Higle & Suvrajeet Sen, 2006. "Multistage stochastic convex programs: Duality and its implications," Annals of Operations Research, Springer, vol. 142(1), pages 129-146, February.
    • Handle: RePEc:spr:annopr:v:142:y:2006:i:1:p:129-146:10.1007/s10479-006-6165-z
    DOI: 10.1007/s10479-006-6165-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-006-6165-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-006-6165-z?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. S. E. Wright, 1994. "Primal-Dual Aggregation and Disaggregation for Stochastic Linear Programs," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 893-908, November.
    2. David R. Cariño & Terry Kent & David H. Myers & Celine Stacy & Mike Sylvanus & Andrew L. Turner & Kouji Watanabe & William T. Ziemba, 1994. "The Russell-Yasuda Kasai Model: An Asset/Liability Model for a Japanese Insurance Company Using Multistage Stochastic Programming," Interfaces, INFORMS, vol. 24(1), pages 29-49, February.
    3. R. T. Rockafellar & Roger J.-B. Wets, 1991. "Scenarios and Policy Aggregation in Optimization Under Uncertainty," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 119-147, February.
    4. John M. Mulvey & Andrzej Ruszczyński, 1995. "A New Scenario Decomposition Method for Large-Scale Stochastic Optimization," Operations Research, INFORMS, vol. 43(3), pages 477-490, June.
    5. Paul H. Zipkin, 1980. "Bounds for Row-Aggregation in Linear Programming," Operations Research, INFORMS, vol. 28(4), pages 903-916, August.
    6. John R. Birge, 1985. "Decomposition and Partitioning Methods for Multistage Stochastic Linear Programs," Operations Research, INFORMS, vol. 33(5), pages 989-1007, October.
    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. Semih Atakan & Suvrajeet Sen, 2018. "A Progressive Hedging based branch-and-bound algorithm for mixed-integer stochastic programs," Computational Management Science, Springer, vol. 15(3), pages 501-540, October.
    2. 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.

    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. Sodhi, ManMohan S. & Tang, Christopher S., 2009. "Modeling supply-chain planning under demand uncertainty using stochastic programming: A survey motivated by asset-liability management," International Journal of Production Economics, Elsevier, vol. 121(2), pages 728-738, October.
    2. ManMohan S. Sodhi, 2005. "LP Modeling for Asset-Liability Management: A Survey of Choices and Simplifications," Operations Research, INFORMS, vol. 53(2), pages 181-196, April.
    3. V.I. Norkin & G.C. Pflug & A. Ruszczynski, 1996. "A Branch and Bound Method for Stochastic Global Optimization," Working Papers wp96065, International Institute for Applied Systems Analysis.
    4. Jacek Gondzio & Roy Kouwenberg, 2001. "High-Performance Computing for Asset-Liability Management," Operations Research, INFORMS, vol. 49(6), pages 879-891, December.
    5. Giovanni Pantuso & Trine K. Boomsma, 2020. "On the number of stages in multistage stochastic programs," Annals of Operations Research, Springer, vol. 292(2), pages 581-603, September.
    6. Semih Atakan & Suvrajeet Sen, 2018. "A Progressive Hedging based branch-and-bound algorithm for mixed-integer stochastic programs," Computational Management Science, Springer, vol. 15(3), pages 501-540, October.
    7. Diana Barro & Elio Canestrelli, 2005. "Time and nodal decomposition with implicit non-anticipativity constraints in dynamic portfolio optimization," GE, Growth, Math methods 0510011, University Library of Munich, Germany.
    8. Gyana R. Parija & Shabbir Ahmed & Alan J. King, 2004. "On Bridging the Gap Between Stochastic Integer Programming and MIP Solver Technologies," INFORMS Journal on Computing, INFORMS, vol. 16(1), pages 73-83, February.
    9. Murwan Siddig & Yongjia Song, 2022. "Adaptive partition-based SDDP algorithms for multistage stochastic linear programming with fixed recourse," Computational Optimization and Applications, Springer, vol. 81(1), pages 201-250, January.
    10. Beltran-Royo, C., 2017. "Two-stage stochastic mixed-integer linear programming: The conditional scenario approach," Omega, Elsevier, vol. 70(C), pages 31-42.
    11. Lijian Chen & Tito Homem-de-Mello, 2010. "Re-solving stochastic programming models for airline revenue management," Annals of Operations Research, Springer, vol. 177(1), pages 91-114, June.
    12. Ankur Kulkarni & Uday Shanbhag, 2012. "Recourse-based stochastic nonlinear programming: properties and Benders-SQP algorithms," Computational Optimization and Applications, Springer, vol. 51(1), pages 77-123, January.
    13. Jie Sun & Xinwei Liu, 2006. "Scenario Formulation of Stochastic Linear Programs and the Homogeneous Self-Dual Interior-Point Method," INFORMS Journal on Computing, INFORMS, vol. 18(4), pages 444-454, November.
    14. C A Poojari & C Lucas & G Mitra, 2008. "Robust solutions and risk measures for a supply chain planning problem under uncertainty," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(1), pages 2-12, January.
    15. Li, Y.P. & Huang, G.H. & Yang, Z.F. & Nie, S.L., 2008. "IFMP: Interval-fuzzy multistage programming for water resources management under uncertainty," Resources, Conservation & Recycling, Elsevier, vol. 52(5), pages 800-812.
    16. Postek, Krzysztof & Romeijnders, Ward & den Hertog, Dick & van der Vlerk, Maartne H., 2016. "Efficient Methods for Several Classes of Ambiguous Stochastic Programming Problems under Mean-MAD Information," Other publications TiSEM a03f895f-b941-41a9-84e0-b, Tilburg University, School of Economics and Management.
    17. Dimitris Bertsimas & Omid Nohadani & Kwong Meng Teo, 2010. "Robust Optimization for Unconstrained Simulation-Based Problems," Operations Research, INFORMS, vol. 58(1), pages 161-178, February.
    18. 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.
    19. Sebastiano Vitali & Ruth Domínguez & Vittorio Moriggia, 2021. "Comparing stage-scenario with nodal formulation for multistage stochastic problems," 4OR, Springer, vol. 19(4), pages 613-631, December.
    20. David R. Cariño & David H. Myers & William T. Ziemba, 1998. "Concepts, Technical Issues, and Uses of the Russell-Yasuda Kasai Financial Planning Model," Operations Research, INFORMS, vol. 46(4), pages 450-462, August.

    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:142:y:2006:i:1:p:129-146:10.1007/s10479-006-6165-z. 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.