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

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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.

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Authors and Affiliations

  1. PhD Student, University of St. Gallen, St. Gallen, Switzerland

    K. Linowsky

  2. Professor, University of Auckland, Auckland, New Zealand

    A. B. Philpott

Authors
  1. K. Linowsky
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  2. A. B. Philpott
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Additional information

Communicated by W. B. Gong

The first author acknowledges support by the Swiss National Science Foundation. The second author acknowledges support by NZPGST Grant UOAX0203. The authors are grateful to the anonymous referees for comments improving the exposition of this paper.

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Linowsky, K., Philpott, A.B. On the Convergence of Sampling-Based Decomposition Algorithms for Multistage Stochastic Programs. J Optim Theory Appl 125, 349–366 (2005). https://doi.org/10.1007/s10957-004-1842-z

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  • DOI: https://doi.org/10.1007/s10957-004-1842-z

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