Distributionally Robust Convex Optimization
Distributionally Robust Convex Optimization
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DOI：
10.1287/opre.2014.1314
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发表时间：
2014-12
期刊：
影响因子：
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通讯作者：
W. Wiesemann;D. Kuhn;Melvyn Sim
中科院分区：
文献类型：
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作者：
W. Wiesemann;D. Kuhn;Melvyn Sim
分布鲁棒优化是在不确定条件下进行决策的一种范式，其中不确定问题数据受概率分布的控制，而概率分布本身又受不确定性的影响。然后假设该分布属于一个模糊集，该模糊集包含与决策者的先验信息兼容的所有分布。在本文中，我们提出了一个统一的框架来建模和求解分布鲁棒优化问题。我们引入标准化的模糊集，它包含所有具有规定的圆锥可表示置信集的分布，并且平均值驻留在仿射流形上。这些歧义集具有很强的表达能力，并将近期文献中的许多歧义集作为特殊情况包含在内。它们还允许我们根据几个经典和/或鲁棒统计指标来表征分布家族，这些指标尚未在鲁棒优化的背景下进行研究。我们确定了基于标准化模糊集的分布鲁棒优化问题在计算上可处理的条件。我们还为违反这些条件的问题提供了易于处理的保守近似。
Distributionally robust optimization is a paradigm for decision making under uncertainty where the uncertain problem data are governed by a probability distribution that is itself subject to uncertainty. The distribution is then assumed to belong to an ambiguity set comprising all distributions that are compatible with the decision maker's prior information. In this paper, we propose a unifying framework for modeling and solving distributionally robust optimization problems. We introduce standardized ambiguity sets that contain all distributions with prescribed conic representable confidence sets and with mean values residing on an affine manifold. These ambiguity sets are highly expressive and encompass many ambiguity sets from the recent literature as special cases. They also allow us to characterize distributional families in terms of several classical and/or robust statistical indicators that have not yet been studied in the context of robust optimization. We determine conditions under which distributionally robust optimization problems based on our standardized ambiguity sets are computationally tractable. We also provide tractable conservative approximations for problems that violate these conditions.