TY - JOUR
T1 - Lipschitz continuity of the solution mapping of symmetric cone complementarity problems
AU - Miao, Xin He
AU - Chen, Jein Shan
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84867820982&partnerID=8YFLogxK
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U2 - 10.1155/2012/130682
DO - 10.1155/2012/130682
M3 - Article
AN - SCOPUS:84867820982
SN - 1085-3375
VL - 2012
JO - Abstract and Applied Analysis
JF - Abstract and Applied Analysis
M1 - 130682
ER -