A Survey and Comparison of Optimization Methods for Solving Multi-Stage Stochastic Programs with Recourse

In the last decade, multi-stage stochastic programs with recourse have been broadly used to model real-world applications. This paper reviews the main optimization methods that are used to solve multi-stage stochastic programs with recourse. In particular, this paper reviews four types of optimization approaches to solve multi-stage stochastic programs with recourse: direct methods, decomposition methods, Lagrangian methods and empirical-distribution methods. All these methods require some form of approximation, since multi-stage stochastic programs involve the evaluation of random functions and their expectations. The authors also provides a classification of the considered optimization methods. While decomposition optimization methods are recommendable for large linear problems, Lagrangian optimization methods are appropriate for highly nonlinear problems. When the problem is both highly nonlinear and very large, an empirical-distribution method may be the best alternative.