Barrier functions in interior point methods
Barrier functions in interior point methods
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DOI：
10.1287/moor.21.4.860
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发表时间：
1996-11-01
影响因子：
1.7
通讯作者：
Guler, O
中科院分区：
文献类型：
--
作者：
Guler, O
我们证明了 Nesterov 和 Nemirovskii 引入的凸锥体的通用势垒函数是锥体特征函数的对数。这种解释证明了在底层锥体的自同构群下通用势垒的不变性。这提供了一种计算均匀锥体通用势垒的简单方法。我们将一些已知的障碍确定为按适当常数缩放的通用障碍。我们还计算了一些新的通用势垒函数。我们的结果将内点方法领域与数学的几个分支联系起来，例如李群、乔丹代数、西格尔域、微分几何、多变量的复分析等。
We show that the universal barrier function of a convex cone introduced by Nesterov and Nemirovskii is the logarithm of the characteristic function of the cone. This interpretation demonstrates the invariance of the universal barrier under the automorphism group of the underlying cone. This provides a simple method for calculating the universal barrier for homogeneous cones. We identify some known barriers as the universal barrier scaled by an appropriate constant. We also calculate some new universal barrier functions. Our results connect the field of interior point methods to several branches of mathematics such as Lie groups, Jordan algebras, Siegel domains, differential geometry, complex analysis of several variables, etc.