Recently there has been much interest in block coordinate descent methods because of their ability to tackle large-scale optimization problems. Multistage stochastic programming problems are an example of very large optimization problems (where the size of the problem grows rapidly with the number of scenarios and time horizon) that display particular structure and sparsity patterns. This work proposes the use of a separable overapproximation to the augmented Lagrangian, which enables a block coordinate descent approach to solving these large convex optimization problems. Preliminary numerical results will also be presented.