The progressive hedging algorithm of Rockafellar and Wets for multistage stochastic programming problems could be viewed as a two-block alternating direction method of multipliers. This correspondence brings in some useful results. In particular, it provides a new proof for the convergence of the progressive hedging algorithm with a flexibility in the selection of primal and dual step lengths and it helps to develop a new progressive hedging algorithm for solving risk averse stochastic optimization problems with cross constraints.

中文翻译：

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多阶段随机最小化问题的渐进式套期保值算法的新解释

对于多阶段随机规划问题，Rockafellar和Wets的渐进式对冲算法可以看作是乘数的两块交替方向方法。这种对应带来一些有用的结果。特别是，它为渐进式对冲算法的收敛性提供了新的证明，并且可以灵活选择原始步长和双重步长，并且有助于开发一种新的渐进式对冲算法，以解决具有交叉约束的风险厌恶随机优化问题。