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首页> 外文期刊>SIAM Journal on Optimization: A Publication of the Society for Industrial and Applied Mathematics >Sampling-based decomposition methods for multistage stochastic programs based on extended polyhedral risk measures
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Sampling-based decomposition methods for multistage stochastic programs based on extended polyhedral risk measures

机译：基于扩展多面体风险测度的多阶段随机程序基于样本的分解方法

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摘要

We define a risk-averse nonanticipative feasible policy for multistage stochastic programs and propose a methodology to implement it. The approach is based on dynamic programming equations written for a risk-averse formulation of the problem. This formulation relies on a new class of multiperiod risk functionals called extended polyhedral risk measures. Dual representations of such risk functionals are given and used to derive conditions of coherence. In the one-period case, conditions for convexity and consistency with second order stochastic dominance are also provided. The risk-averse dynamic programming equations are specialized considering convex combinations of one-period extended polyhedral risk measures such as spectral risk measures. To implement the proposed policy, the approximation of the risk-averse recourse functions for stochastic linear programs is discussed. In this context, we detail a stochastic dual dynamic programming algorithm which converges to the optimal value of the risk-averse problem.
机译：我们为多阶段随机计划定义了一种规避风险的非预期可行策略，并提出了实施该策略的方法。该方法基于为问题的规避风险而编写的动态编程方程式。这种表述依赖于称为扩展多面体风险度量的一类新的多周期风险功能。给出了此类风险功能的双重表示，并用于导出一致性条件。在一个周期的情况下，还提供了具有二阶随机优势的凸性和一致性的条件。规避风险的动态规划方程是专门考虑一周期扩展多面体风险度量（例如频谱风险度量）的凸组合。为了实施所提出的策略，讨论了针对随机线性规划的风险规避追索函数的逼近。在这种情况下，我们详细介绍了一种随机双动态规划算法，该算法收敛到规避风险的最优值。

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