Gordon's inequality and condition numbers in conic optimization
Gordon's inequality and condition numbers in conic optimization
复制标题
圆锥优化中的戈登不等式和条件数
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Martin Lotz
中科院分区：
文献类型：
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作者：
Dennis Amelunxen;Martin Lotz
条件数的概率分析传统上是从不同角度进行的；一种基于复杂性理论中的斯梅尔规划，以积分几何为特色，而另一种由几何泛函分析推动，并利用高斯过程理论。在本文中，我们在双锥齐次可行性问题以及由锥优化理论所激发的条件数的背景下，探索这两种方法之间的联系。分析中的关键工具是针对高斯过程的斯莱皮恩和戈登比较不等式（被解释为矩泛函的单调性性质），以及它们与锥积分几何思想的相互作用。
The probabilistic analysis of condition numbers has traditionally been approached from different angles; one is based on Smale's program in complexity theory and features integral geometry, while the other is motivated by geometric functional analysis and makes use of the theory of Gaussian processes. In this note we explore connections between the two approaches in the context of the biconic homogeneous feasiblity problem and the condition numbers motivated by conic optimization theory. Key tools in the analysis are Slepian's and Gordon's comparision inequalities for Gaussian processes, interpreted as monotonicity properties of moment functionals, and their interplay with ideas from conic integral geometry.
DOI：
10.1090/surv/089
发表时间：
2001
期刊：
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影响因子：
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作者：
M. Ledoux
通讯作者：
M. Ledoux