Linear Complementarity Problems over Symmetric Cones: Characterization of Qb-transformations and Existence Results

被引：1

作者：

Lopez, Julio ^{[1
]}

Lopez, Ruben ^{[2
]}

Ramirez, Hector C. ^{[3
]}

机构：

[1] Univ Tecn Federico Santa Maria, Dept Matemat, Vicuna Mackenna 3939, Santiago, Chile

[2] Univ Catolica Santisima Concepcion, Dept Matemat & Fis Aplicadas, Concepcion, Chile

[3] Univ Chile, FCFM, Ctr Modelamiento Matemat CNRS UMI 2807, Dept Ingn Matemat, Santiago, Chile

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2013年 / 159卷 / 03期

关键词：

Euclidean Jordan algebra; Linear complementarity problem; Symmetric cone; Q(b)-transformation; Q-transformation; Garcia's transformation; P-PROPERTIES; Q-MATRICES; TRANSFORMATIONS;

D O I：

10.1007/s10957-012-0116-4

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：

This paper is devoted to the study of the symmetric cone linear complementarity problem (SCLCP). Specifically, our aim is to characterize the class of linear transformations for which the SCLCP has always a nonempty and bounded solution set in terms of larger classes. For this, we introduce a couple of new classes of linear transformations in this SCLCP context. Then, we study them for concrete particular instances (such as second-order and semidefinite linear complementarity problems) and for specific examples (Lyapunov, Stein functions, among others). This naturally permits to establish coercive and noncoercive existence results for SCLCPs.

引用

页码：741 / 768

页数：28

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