摘要
本文研究n阶实对称矩阵A的前m项最大特征值之和fm(A)的非光滑分析问题.利用Ky-Fan的关于特征值之和的变分原理以及凸分析理论,得到了fm(A)的次梯度和方向导数的显式表达式.
Let A be an n- by-n symmetric matrix. We study in this paper a problemof nonsmooth analysis of fm(A), defined as the sum of the m largest eigenvalues of A. Basingon the Ky-Fan's variational principle for fm(A) and the techniques from convex analysis, wederive explicit formulas for the subdifferential as well as the directional derivative of the sumfm(A) viewed as a function of A.
出处
《系统科学与数学》
CSCD
北大核心
1997年第2期156-164,共9页
Journal of Systems Science and Mathematical Sciences
关键词
对称矩阵
特征值
和
非光滑分析
Symmetric matrix, sums of eigenvalues, nonsmooth analysis.