Lipschitz Continuity of the Solution Mapping of Symmetric Cone Complementarity Problems. (20th September 2012)

• Record Type: Journal Article
• Authors: Miao, Xin-He; Chen, Jein-Shan
• Other Names: Zizovic Malisa R. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-09-20
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/130682
• Languages: English
• ISSNs: 1085-3375

Abstract

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.