On regularization with normal solutions in decomposition methods for multistage stochastic programming

We consider well-known decomposition techniques for multistage stochastic programming and a new scheme based on normal solutions for stabilizing calculations as the iteration process progresses. The given algorithms combine ideas from finite perturbation of convex programs and level bundle methods to regularize the so-called forward step of these decomposition methods. In contrast to other regularized approaches for multistage programs, the given algorithms do not suffer from the effect of bad quality incumbent points. We also improve the backward step (that generates cuts, approximating the cost-togo functions) by employing an adaptive partition-based approach to reduce the computational burden. Numerical experiments on a hydrothermal scheduling problem indicate that our second algorithm exhibits significantly faster convergence than the classical Stochastic Dual Dynamic Programming algorithm.