The same growth of FB and NR symmetric cone complementarity functions

被引：5

作者：

Bi, Shujun ^{[2
]}

Pan, Shaohua ^{[2
]}

Chen, Jein-Shan ^{[1
]}

机构：

[1] Natl Taiwan Normal Univ, Dept Math, Taipei 11677, Taiwan

[2] S China Univ Technol, Dept Math, Guangzhou 510640, Peoples R China

来源：

OPTIMIZATION LETTERS | 2012年 / 6卷 / 01期

关键词：

Symmetric cone; FB and NR complementarity functions; Growth; EUCLIDEAN JORDAN ALGEBRAS; INTERIOR-POINT ALGORITHMS; MERIT FUNCTIONS; LINEAR TRANSFORMATIONS;

D O I：

10.1007/s11590-010-0257-z

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We establish that the Fischer-Burmeister (FB) complementarity function and the natural residual (NR) complementarity function associated with the symmetric cone have the same growth, in terms of the classification of Euclidean Jordan algebras. This, on the one hand, provides an affirmative answer to the second open question proposed by Tseng (J Optim Theory Appl 89:17-37, 1996) for the matrix-valued FB and NR complementarity functions, and on the other hand, extends the third important inequality of Lemma 3.1 in the aforementioned paper to the setting of Euclidean Jordan algebras. It is worthwhile to point out that the proof is surprisingly simple.

引用

页码：153 / 162

页数：10

共 23 条

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