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Lingchen Kong (konglchen126.com) Abstract: We consider existence and uniqueness properties of a solution to homogeneous cone complementarity problem (HCCP). Employing the $T$algebraic characterization of homogeneous cones, we generalize the $P, P_0, R_0$ properties for a nonlinear function associated with the standard nonlinear complementarity problem to the setting of HCCP. We prove that if a continuous function has either the order$P_0$ and $R_0$, or the $P_0$ and $R_0$ properties then all the associated HCCPs have solutions. In particular, if a continuous function has the trace$P$ property then the associated HCCP has a unique solution (if any); if it has the uniformtrace$P$ property then the associated HCCP has the global uniqueness (of the solution) property (GUS). We present a necessary condition for a nonlinear transformation to have the GUS property. Moreover, we establish a global error bound for the HCCP with the uniformtrace$P$ property. Finally, we study the HCCP with the relaxation transformation on a $T$algebra and automorphism invariant properties for homogeneous cone linear complementarity problem. Keywords: Homogeneous cone complementarity problem, $P$ property, existence of a solution, globally uniquely solvability property, error bound Category 1: Complementarity and Variational Inequalities Citation: Research Report, April 2009. Download: [PDF] Entry Submitted: 04/13/2009 Modify/Update this entry  
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