SIAM Journal on Optimization, Volume 30, Issue 3, Page 2083-2102, January 2020.
In some applications the considered multistage stochastic programs have a periodical behavior. We show that in such cases it is possible to drastically reduce the number of stages by introducing a periodical analogue of the so-called Bellman equations for discounted infinite horizon problems used in Markov decision processes and stochastic optimal control. Furthermore, we describe a variant of the stochastic dual dynamic programming algorithm, applied to the constructed periodical Bellman equations, and provide numerical experiments for the Brazilian interconnected power system problem.

中文翻译：

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定期多阶段随机程序

SIAM优化杂志，第30卷，第3期，第2083-2102页，2020
年1月。在某些应用程序中，考虑的多阶段随机程序具有周期性。我们表明，在这种情况下，有可能通过引入所谓的Bellman方程的周期类似物来大幅度减少阶段数，该Bellman方程用于马尔可夫决策过程和随机最优控制中的贴现无限视界问题。此外，我们描述了一种随机双动态规划算法的变体，该变体应用于构造的周期性Bellman方程，并提供了巴西互连电力系统问题的数值实验。