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Title: Second-order directional derivatives of spectral functions
Authors: Li, SJ
Teo, KL
Yang, XQ 
Keywords: Nonsmooth analysis
Second-order directional derivative
Spectral function
Issue Date: 2005
Publisher: Pergamon Press
Source: Computers and mathematics with applications, 2005, v. 50, no. 5-6, p. 947-955 How to cite?
Journal: Computers and mathematics with applications 
Abstract: A spectral function of a symmetric matrix X is a function which depends only on the eigenvalues of X, λ1 (X) < λ 2(X) << λn (X), and may be written as f (λ1 (X), λ2(X), , λn (X)) for some symmetric function f. In this paper, we assume that f is a C 1,1 function and discuss second-order directional derivatives of such a spectral function. We obtain an explicit expression of second-order directional derivative for the spectral function.
ISSN: 0898-1221
EISSN: 1873-7668
DOI: 10.1016/j.camwa.2004.11.021
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