Properties Of The Solution Of Symmetric Cone Complementarity Problems

This paper discusses the properties of the solution of symmetric cone complementarity problems(SCCPs).The main content includes two aspects. Firstly, we consider the general SCCP. By using the introduced concept of exceptional family of elements for the SCCP, we first establish a general existence theorem for the SCCP, and then investigate several sufficient con-ditions on the existence of a solution to the SCCP, including monotonicity condition,Karamardian condition,and coercivity condition.Secondly, we consider the symmetric cone linear complementarity problems with a Carte-sian P*(κ)-transformation,which is denoted by the Cartesian P*(κ)-SCLCP. We establish a general existence theorem for the Cartesian P*(κ)-SCLCP. Then we show that the solution set of the Cartesian P*(κ)-SCLCP is convex if it is nonempty; and that the solution set of the Cartesian P*(κ)-SCLCP is nonempty and compact if the problem concerned has a strictly feasible solution.In the analysis of this paper,the theory of Euclidean Jordan algebras is a main tool.