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

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.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.