The talk describes how and nested Benders and scenario decomposition methods, used for solving multistage stochastic programs with recourse, can be adapted to decompose the scenario tree into arbitrarily shaped subtrees. Prior adaptions have been limited in their generality: clusters of scenarios for scenario decomposition methods and subtrees formed by combining stages for the node-based nested Benders decomposition method.
Here, the scenario tree is decomposed using an arbitrary cover or partition of subtrees. The approach leads to classes of methods which include the current implementations' of the various algorithms. This subtree decomposition methodology could potentially be applied to a number of other existing stochastic programming algorithms.
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