Robust Solutions of Optimization Problems Affected by Uncertain Probabilities
Robust Solutions of Optimization Problems Affected by Uncertain Probabilities
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DOI：
10.1287/mnsc.1120.1641
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发表时间：
2013-02-01
影响因子：
5.4
通讯作者：
Rennen, Gijs
中科院分区：
文献类型：
--
作者：
Ben-Tal, Aharon;den Hertog, Dick;Rennen, Gijs
在本文中，我们专注于鲁棒线性优化问题的不确定性区域定义的φ发散（例如，卡方，Hellinger，Kullback-Leibler）。我们展示了如何不确定性区域的基础上，φ发散出现在一个自然的方式作为置信集，如果不确定的参数包含的概率向量的元素。这样的问题经常发生在，例如，在库存控制或金融，涉及条款包含随机变量的时刻，预期效用等的优化问题，我们表明，强大的对应的线性优化问题与φ发散不确定性是易于处理的，通常在文献中考虑的φ的选择。我们扩展的结果是非线性的优化变量的问题。几个应用程序，包括资产定价的例子和数值多项报童的例子，说明了所提出的方法的相关性。
In this paper we focus on robust linear optimization problems with uncertainty regions defined by phi-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on phi-divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization problems in inventory control or finance that involve terms containing moments of random variables, expected utility, etc. We show that the robust counterpart of a linear optimization problem with phi-divergence uncertainty is tractable for most of the choices of phi typically considered in the literature. We extend the results to problems that are nonlinear in the optimization variables. Several applications, including an asset pricing example and a numerical multi-item newsvendor example, illustrate the relevance of the proposed approach.