两阶段随机线性规划的广义自适应划分方法：收敛性和推广性
Generalized adaptive partition-based method for two-stage stochastic linear programs : convergence and generalization
摘要：
自适应分区方法（APM）是求解两阶段随机线性问题（2SLP）的数值方法。其核心思想是迭代地构建一个适应的分区空间的alea，以聚合的情况下，同时保存的真实价值的成本去当前的第一阶段控制。利用对偶容许集的正规扇，将经典的APM方法推广到几乎任意的2SLP，给出了划分适应于非有限分布的充要条件，证明了方法的收敛性.我们通过将APM与L形算法联系起来，给出了一些额外的见解。
英文摘要：
Adaptive Partition-based Methods (APM) are numerical methods to solve two-stage stochastic linear problems (2SLP). The core idea is to iteratively construct an adapted partition of the space of alea in order to aggregate scenarios while conserving the true value of the cost-to-go for the current first-stage control. Relying on the normal fan of the dual admissible set, we extend the classical and generalized APM method by i) extending the method to almost arbitrary 2SLP, ii) giving a necessary and sufficient condition for a partition to be adapted even for non-finite distribution, and iii) proving the convergence of the method. We give some additional insights by linking APM to the L-shaped algorithm.
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