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.
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