Strong semismoothness of the fischer-burmeister SDC and SOC complementarity functions

被引：110

作者：

Sun, DF ^{[1
]}

Sun, J

机构：

[1] Natl Univ Singapore, Dept Math, Singapore 117548, Singapore

[2] Natl Univ Singapore, Sch Business, Singapore 117548, Singapore

[3] Natl Univ Singapore, MIT Alliance, Singapore 117548, Singapore

来源：

MATHEMATICAL PROGRAMMING | 2005年 / 103卷 / 03期

关键词：

Fischer-Burmeister function; SDC; SOC; SVD; strong semismoothness;

D O I：

10.1007/s10107-005-0577-4

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We show that the Fischer-Burmeister complementarity functions, associated to the semidefinite cone (SDC) and the second order cone (SOC), respectively, are strongly semismooth everywhere. Interestingly enough, the proof relys on a relationship between the singular value decomposition of a nonsymmetric matrix and the spectral decomposition of a symmetric matrix.

引用

页码：575 / 581

页数：7

共 19 条

[1] Second order optimality conditions based on parabolic second order tangent sets [J].

Bonnans, JF ;

Cominetti, R ;

Shapiro, A .

SIAM JOURNAL ON OPTIMIZATION, 1999, 9 (02) :466-492

[2]

Borwein J. M., 2000, CMS BOOKS MATH

[3] Analysis of nonsmooth vector-valued functions associated with second-order cones [J].

Chen, JS ;

Chen, X ;

Tseng, P .

MATHEMATICAL PROGRAMMING, 2004, 101 (01) :95-117

[4] Non-interior continuation methods for solving semidefinite complementarity problems [J].

Chen, X ;

Tseng, P .

MATHEMATICAL PROGRAMMING, 2003, 95 (03) :431-474

[5] Analysis of nonsmooth symmetric-matrix-valued functions with applications to semidefinite complementarity problems [J].

Chen, X ;

Qi, HD ;

Tseng, P .

SIAM JOURNAL ON OPTIMIZATION, 2003, 13 (04) :960-985

[6] Complementarity functions and numerical experiments on some smoothing newton methods for second-order-cone complementarity problems [J].

Chen, XD ;

Sun, D ;

Sun, J .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2003, 25 (1-3) :39-56

[7] Inverse eigenvalue problems [J].

Chu, MT .

SIAM REVIEW, 1998, 40 (01) :1-39

[8] Solution of monotone complementarity problems with locally Lipschitzian functions [J].

Fischer, A .

MATHEMATICAL PROGRAMMING, 1997, 76 (03) :513-532

[9]

Fischer A., 1992, Optimization, V24, P269, DOI 10.1080/02331939208843795

[10]

Fukushima M, 2001, SIAM J OPTIMIZ, V12, P436

← 1 2 →