Sufficiency of linear transformations on Euclidean Jordan algebras

被引：9

作者：

Qin, Linxia ^{[1
]}

Kong, Lingchen ^{[1
,2
]}

Han, Jiye ^{[3
]}

机构：

[1] Beijing Jiaotong Univ, Dept Appl Math, Beijing 100044, Peoples R China

[2] Univ Waterloo, Dept Combinator & Optimizat, Fac Math, Waterloo, ON N2L 3G1, Canada

[3] Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China

来源：

OPTIMIZATION LETTERS | 2009年 / 3卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Linear transformation; Euclidean Jordan algebra; Column-sufficiency; Row-sufficiency; COMPLEMENTARITY-PROBLEMS; SYMMETRIC CONES; P-PROPERTIES; MATRICES;

D O I：

10.1007/s11590-008-0106-5

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 extend the row-sufficiency and column-sufficiency of a linear transformation from R(n) to the setting of Euclidean Jordan algebras. For linear complementarity problems over symmetric cones, we show that the column-sufficiency along with Cross Commutative property is equivalent to the convexity of the solution set, while the row-sufficiency is necessary for the existence of solutions under some conditions.

引用

页码：265 / 276

页数：12

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