Stochastic programming and control theory in multistage optimization problems

Multistage stochastic optimization aims at finding optimal decision strategies in situations where the dynamic and stochastic components are interrelated. Stochastic programming and discrete time optimal control are approaches widely used to solve such problems. Thus a combination of the two methods appears to be interesting to efficiently solve dynamic stochastic optimization problems in discrete time. To cope with the uncertain quantities we consider a scenario approach and write the stochastic problem in its arborescent form. This approach allows to obtain a double decomposition with respect to time stages and with respect to nodes in each time stage. This method, already applied to efficiently solve quadratic problems, can be applied to a broader class of multistage stochastic programming problem which can be written in the framework of discrete time stochastic optimal control problem.