Clarke generalized Jacobian of the projection onto the cone of positive semidefinite matrices

被引：34

作者：

Malick, Jerome ^{[1
]}

Sendov, Hristo S.

机构：

[1] INRIA, F-38334 Saint Ismier, France

[2] Univ Guelph, Dept Math & Stat, Guelph, ON N1G 2W1, Canada

来源：

SET-VALUED ANALYSIS | 2006年 / 14卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Clarke generalized Jacobian; differentiability eigenvalue optimization; nonsmooth analysis; perturbation theory; positive semidefinite matrices; projection spectral function;

D O I：

10.1007/s11228-005-0005-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

This paper studies the differentiability properties of the projection onto the cone of positive semidefinite matrices. In particular, the expression of the Clarke generalized Jacobian of the projection at any symmetric matrix is given.

引用

页码：273 / 293

页数：21

共 14 条

[1]

Clarke FH, 1983, OPTIMIZATION NONSMOO

[2]

Davis C, 1957, Arch. Math. (Basel), V8, P276

[3]

EVANS LC, 1992, STUD ADV MATH CRC

[4]

COMPUTING A NEAREST SYMMETRIC POSITIVE SEMIDEFINITE MATRIX [J].