We prove the almost-sure convergence of a class of sampling-based 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 stochastic dual dynamic programming, cutting-plane and partial-sampling CUPPS algorithm, and dynamic outer-approximation sampling algorithms when applied to problems with general convex cost functions.
['Pierre Girardeau', 'Vincent Leclère', 'Andrew B. Philpott']
On the Convergence of Decomposition Methods for Multistage Stochastic Convex Programs