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On the Convergence of Sampling-Based Decomposition Algorithms for Multistage Stochastic Programs

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  • K. Linowsky

    (University of St. Gallen)

  • A. B. Philpott

    (University of Auckland)

Abstract

The paper presents a convergence proof for a broad class of sampling algorithms for multistage stochastic linear programs in which the uncertain parameters occur only in the constraint right-hand sides. This class includes SDDP, AND, ReSa, and CUPPS. We show that, under some independence assumptions on the sampling procedure, the algorithms converge with probability 1.

Suggested Citation

  • K. Linowsky & A. B. Philpott, 2005. "On the Convergence of Sampling-Based Decomposition Algorithms for Multistage Stochastic Programs," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 349-366, May.
    • Handle: RePEc:spr:joptap:v:125:y:2005:i:2:d:10.1007_s10957-004-1842-z
    DOI: 10.1007/s10957-004-1842-z
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    References listed on IDEAS

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    1. Z. L. Chen & W. B. Powell, 1999. "Convergent Cutting-Plane and Partial-Sampling Algorithm for Multistage Stochastic Linear Programs with Recourse," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 497-524, September.
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    Cited by:

    1. de Queiroz, Anderson Rodrigo, 2016. "Stochastic hydro-thermal scheduling optimization: An overview," Renewable and Sustainable Energy Reviews, Elsevier, vol. 62(C), pages 382-395.
    2. Haoxiang Yang & Harsha Nagarajan, 2022. "Optimal Power Flow in Distribution Networks Under N – 1 Disruptions: A Multistage Stochastic Programming Approach," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 690-709, March.
    3. Wim Ackooij & Welington Oliveira & Yongjia Song, 2019. "On level regularization with normal solutions in decomposition methods for multistage stochastic programming problems," Computational Optimization and Applications, Springer, vol. 74(1), pages 1-42, September.
    4. Saif Benjaafar & Daniel Jiang & Xiang Li & Xiaobo Li, 2022. "Dynamic Inventory Repositioning in On-Demand Rental Networks," Management Science, INFORMS, vol. 68(11), pages 7861-7878, November.
    5. P. Girardeau & V. Leclere & A. B. Philpott, 2015. "On the Convergence of Decomposition Methods for Multistage Stochastic Convex Programs," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 130-145, February.
    6. Arnab Bhattacharya & Jeffrey P. Kharoufeh & Bo Zeng, 2023. "A Nonconvex Regularization Scheme for the Stochastic Dual Dynamic Programming Algorithm," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1161-1178, September.
    7. 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.
    8. Shapiro, Alexander, 2011. "Analysis of stochastic dual dynamic programming method," European Journal of Operational Research, Elsevier, vol. 209(1), pages 63-72, February.
    9. Soares, Murilo Pereira & Street, Alexandre & Valladão, Davi Michel, 2017. "On the solution variability reduction of Stochastic Dual Dynamic Programming applied to energy planning," European Journal of Operational Research, Elsevier, vol. 258(2), pages 743-760.
    10. Martin Šmíd & Václav Kozmík, 2024. "Approximation of multistage stochastic programming problems by smoothed quantization," Review of Managerial Science, Springer, vol. 18(7), pages 2079-2114, July.
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