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

Xin He Miao, Jein Shan Chen

Research output: Contribution to journalArticlepeer-review

Abstract

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).

Original languageEnglish
Pages (from-to)271-294
Number of pages24
JournalLinear Algebra and Its Applications
Volume613
DOIs
Publication statusAccepted/In press - 2020

Keywords

  • Absolute value equations
  • Globally uniquely solvable property
  • P-property
  • Second-order cone linear complementarity problem

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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