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Duality and optimality in multistagestochastic programming

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  • 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

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  • 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
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    Cited by:

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

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