  We introduce StoDCuP (Stochastic Dynamic Cutting Plane), an extension of the
Stochastic Dual Dynamic Programming (SDDP) algorithm to solve multistage
stochastic convex optimization problems. At each iteration, the algorithm
builds lower affine functions not only for the cost-to-go functions, as SDDP
does, but also for some or all nonlinear cost and constraint functions. We show
the almost sure convergence of StoDCuP. We also introduce an inexact variant of
StoDCuP where all subproblems are solved approximately (with bounded errors)
and show the almost sure convergence of this variant for vanishing errors.
