We introduce Stochastic Dynamic Cutting Plane (StoDCuP), an extension of the Stochastic Dual Dynamic Programming (SDDP) algorithm to solve multistage stochastic convex optimization problems. At each iteration, the algorithm builds lower bounding 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. Finally, numerical experiments are presented on nondifferentiable multistage stochastic programs where Inexact StoDCuP computes a good approximate policy quicker than StoDCuP while SDDP and the previous inexact variant of SDDP combined with Mosek library to solve subproblems were not able to solve the differentiable reformulation of the problem.

我们介绍了随机动态切割平面（StoDCuP），它是随机双重动态规划（SDDP）算法的扩展，可以解决多阶段随机凸优化问题。在每次迭代中，该算法不仅会像SDDP一样为待销成本函数构建下界仿射函数，而且还会为某些或所有非线性成本和约束函数构建下界仿射函数。我们展示了StoDCuP几乎可以肯定的收敛。我们还介绍了一个StoDCuP的不精确变体，其中所有子问题都得到了近似解决（带有有限误差），并显示了该变体几乎确定的收敛性，以消除错误。最后，