On the Convergence of Decomposition Methods for Multistage Stochastic Convex Programs

@article{Girardeau2015OnTC,
  title={On the Convergence of Decomposition Methods for Multistage Stochastic Convex Programs},
  author={Pierre Girardeau and Vincent Lecl{\`e}re and Andrew B. Philpott},
  journal={Math. Oper. Res.},
  year={2015},
  volume={40},
  pages={130-145}
}
We prove the almost-sure convergence of a class of samplingbased nested decomposition algorithms for multistage stochastic convex programs in which the stage costs are general convex functions of the decisions, and uncertainty is modelled by a scenario tree. As special cases, our results imply the almost-sure convergence of SDDP, CUPPS and DOASA when applied to problems with general convex cost functions. 

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