经典拟牛顿法超线性收敛的新结果
New Results on Superlinear Convergence of Classical Quasi-Newton Methods.
作者信息
Rodomanov Anton, Nesterov Yurii
机构信息
ICTEAM, Catholic University of Louvain, Louvain-la-Neuve, Belgium.
CORE, Catholic University of Louvain, Louvain-la-Neuve, Belgium.
出版信息
J Optim Theory Appl. 2021;188(3):744-769. doi: 10.1007/s10957-020-01805-8. Epub 2021 Jan 9.
We present a new theoretical analysis of local superlinear convergence of classical quasi-Newton methods from the convex Broyden class. As a result, we obtain a significant improvement in the currently known estimates of the convergence rates for these methods. In particular, we show that the corresponding rate of the Broyden-Fletcher-Goldfarb-Shanno method depends only on the product of the dimensionality of the problem and the of its condition number.
我们对来自凸布罗伊登类的经典拟牛顿法的局部超线性收敛性进行了新的理论分析。结果，我们在这些方法当前已知的收敛速度估计方面取得了显著改进。特别地，我们表明布罗伊登 - 弗莱彻 - 戈德法布 - 香农方法的相应收敛速度仅取决于问题的维度与其条件数的 之积。 （注：原文中“the of its condition number”这里有缺失信息）
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