On matrix characterizations for P-property of the linear transformation in second-order cone linear complementarity problems

The P-property of the linear transformation in second-order cone linear complementarity problems (SOCLCP) plays an important role in checking the globally uniquely solvable (GUS) property due to the work of Gowda et al. However, it is not easy to verify the P-property of the linear transformation, i...

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Bibliographic Details
Published in:Linear algebra and its applications 2021-03, Vol.613, p.271-294
Main Authors: Miao, Xin-He, Chen, Jein-Shan
Format: Article
Language:English
Subjects:
Absolute value equations
Globally uniquely solvable property
Linear algebra
Linear transformations
Mathematical analysis
Matrix methods
P-property
Second-order cone linear complementarity problem
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Summary:The P-property of the linear transformation in second-order cone linear complementarity problems (SOCLCP) plays an important role in checking the globally uniquely solvable (GUS) property due to the work of Gowda et al. However, it is not easy to verify the P-property of the linear transformation, in general. In this paper, we provide matrix characterizations for checking the P-property, which is a new approach different from those in the literature. This is a do-able manipulation, which helps verifications of the P-property and globally uniquely solvable (GUS) property in second-order cone linear complementarity problems. Moreover, using an equivalence relation to the second-order cone linear complementarity problem, we study some sufficient and necessary conditions for the unique solution of the absolute value equations associated with second-order cone (SOCAVE).
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2020.11.010