Recursive Direct Optimization and Successive Refinement in Multistage Stochastic Programs

The paper presents a new algorithmic approach for multistage stochastic programs which are seen as discrete optimal control problems with a characteristic dynamic structure induced by the scenario tree. To exploit that structure, we propose a highly eecient dynamic programming recursion for the computationally intensive task of KKT systems solution within a primal-dual interior point method. Convergence is drastically enhanced by a successive reenement technique providing both primal and dual initial estimates. Test runs on a multistage portfolio selection problem demonstrate the performance of the method.