  We propose a new algorithm for solving multistage stochastic mixed integer
linear programming (MILP) problems with complete continuous recourse. In a
similar way to cutting plane methods, we construct nonlinear Lipschitz cuts to
build lower approximations for the non-convex cost to go functions. An example
of such a class of cuts are those derived using Augmented Lagrangian Duality
for MILPs. The family of Lipschitz cuts we use is MILP representable, so that
the introduction of these cuts does not change the class of the original
stochastic optimization problem.
  We illustrate the application of this algorithm on two simple case studies,
comparing our approach with the convex relaxation of the problems, for which we
can apply SDDP, and for a discretized approximation, applying SDDiP.
