AI 中文总结
该研究从原始视角提出BiCS算法框架，用于处理复杂结构下的分布鲁棒优化问题，实验表明其性能优异，可求解部分现有方法难以处理的情形。
AI 中文摘要
分布鲁棒优化（DRO）作为一种流行的优化方案，可保护决策免受概率分布的不确定性影响。对于（单阶段）DRO，当模型或不确定集结构复杂时，主流的对偶重述可能变得难以处理。我们从原始视角研究DRO，直接处理闭集、可能无界样本空间上的不确定集中的分布。该视角催生了名为BiCS的算法框架，它通过构造和利用分布割集实现优异性能。我们证明BiCS适用于标准DRO、几乎必然DRO、含各类机会约束的DRO，以及通过局部信息增强的不确定集的DRO。针对矩和Wasserstein不确定集的数值实验显示，该框架表现出优异性能，包括可求解所考察的紧凑重述不可用或计算困难的情形，且局部信息研究可直接展现最坏情况分布的变化。
英文摘要
As a popular optimization scheme, distributionally robust optimization (DRO) protects decisions against ambiguity in probability distributions. For (single-stage) DRO, prevailing dual reformulations can become difficult when model or ambiguity-set structures are complex. We study DRO from a primal perspective, working directly with distributions in ambiguity sets on closed, potentially unbounded sample spaces. This perspective leads to an algorithmic framework, referred to as BiCS, that constructs and leverages distribution cuts to achieve strong performance. We show that BiCS is applicable to standard DRO, almost-sure DRO, DRO with various chance constraints, and DRO with ambiguity sets strengthened by local information. Numerical experiments with moment and Wasserstein ambiguity sets show that this framework demonstrates superior performance, including solving cases where the examined compact reformulations are unavailable or computationally difficult. The local-information study also makes changes in worst-case distributions directly visible.
Comments63 pages, 7 figures, 18 tables
