A distributionally robust perspective on uncertainty quantification and chance constrained programming
A distributionally robust perspective on uncertainty quantification and chance constrained programming
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DOI：
10.1007/s10107-015-0896-z
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发表时间：
2015-03
影响因子：
2.7
通讯作者：
G. A. Hanasusanto;Vladimir Roitch;D. Kuhn;W. Wiesemann
中科院分区：
文献类型：
--
作者：
G. A. Hanasusanto;Vladimir Roitch;D. Kuhn;W. Wiesemann
不确定性量化的目的是证明给定的物理、工程或经济系统以高概率满足多个安全条件。更远大的目标是积极地影响系统，以保证和维护系统的安全，这种情况可以通过机会约束程序来建模。在本文中，我们假设系统的参数由一个模糊分布控制，该分布只属于一个模糊集，通过广义矩界和结构性质（如对称、单模或独立模式）来表征。在避免歧义的不确定性量化和机会约束规划中，我们描述了易处理性和难处理性之间的分水岭。利用分布鲁棒优化的工具，我们导出了可处理问题类的显式二次公式，并提出了可有效计算的可处理问题类的保守近似。
The objective of uncertainty quantification is to certify that a given physical, engineering or economic system satisfies multiple safety conditions with high probability. A more ambitious goal is to actively influence the system so as to guarantee and maintain its safety, a scenario which can be modeled through a chance constrained program. In this paper we assume that the parameters of the system are governed by an ambiguous distribution that is only known to belong to an ambiguity set characterized through generalized moment bounds and structural properties such as symmetry, unimodality or independence patterns. We delineate the watershed between tractability and intractability in ambiguity-averse uncertainty quantification and chance constrained programming. Using tools from distributionally robust optimization, we derive explicit conic reformulations for tractable problem classes and suggest efficiently computable conservative approximations for intractable ones.