Convex Optimal Uncertainty Quantification
Convex Optimal Uncertainty Quantification
复制标题
凸最优不确定性量化
DOI：
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发表时间：
2013
影响因子：
3.1
通讯作者：
R. Murray
中科院分区：
文献类型：
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作者：
Shuo Han;Molei Tao;U. Topcu;H. Owhadi;R. Murray
最优不确定性量化 (OUQ) 是一种对随机系统进行数值极端情况分析的框架，对潜在概率分布的了解并不完善。本文提出了将 OUQ 问题重新表述为有限维凸优化问题的充分条件，从而可以获得有效的数值解。充分条件包括目标函数是分段凹的并且约束是分段凸的。特别是，我们表明分段凹目标函数可能出现在目标由参数化线性程序的最优值定义的应用中。
Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an OUQ problem can be reformulated as a finite-dimensional convex optimization problem, for which efficient numerical solutions can be obtained. The sufficient conditions include that the objective function is piecewise concave and the constraints are piecewise convex. In particular, we show that piecewise concave objective functions may appear in applications where the objective is defined by the optimal value of a parameterized linear program.