Lipschitz continuity of the solution mapping of symmetric cone complementarity problems

Xin He Miao, Jein Shan Chen

Research output: Contribution to journalArticle

Abstract

This paper investigates the Lipschitz continuity of the solution mapping of symmetric cone (linear or nonlinear) complementarity problems (SCLCP or SCCP, resp.) over Euclidean Jordan algebras. We show that if the transformation has uniform Cartesian P-property, then the solution mapping of the SCCP is Lipschitz continuous. Moreover, we establish that the monotonicity of mapping and the Lipschitz continuity of solutions of the SCLCP imply ultra P-property, which is a concept recently developed for linear transformations on Euclidean Jordan algebra. For a Lyapunov transformation, we prove that the strong monotonicity property, the ultra P-property, the Cartesian P-property, and the Lipschitz continuity of the solutions are all equivalent to each other.

Original languageEnglish
Article number130682
JournalAbstract and Applied Analysis
Volume2012
DOIs
Publication statusPublished - 2012

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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