Solvability Of Symmetric Cone Complementarity Problems

Symmetric cone complementarity problem (SCCP) includes the nonnega,tive orthant nonlinear complementarity problem (NCP), the second-order cone complementarity problem (SOCCP), and the semi-definite complementarity problem (SDCP). This model provides a simple, natural, and unified framework. It has wide applications in engineering, economics, management science, and other fields. By employing the technique of Euclidean Jordan algebra, we get many embedded results. This thesis is mainly concerned with the solvability of the SCCP.There are three chapters in this thesis.Since Euclidean Jordan algebra technique provides a, powerful tool for describing the structure of symmetric cones and sequentially solving symmetric cone optimization problems, in Chapter 1, we recalled some basic concepts and useful results of Euclidean Jordan algebras. Then we introduced the symmetric cone complementarity problem.In Chapter 2, we introduced the solvability results of SCCP. After briefly stated some important properties with regards to the solvability of standard complementarity problem, we give the sufficiency of linear transformations on Euclidean Jordan algebras, and show that they have close connection with the existence and convexity of the solution set of SCCP.In Chapter 3, the main conclusions and innovation of this thesis are summarized, and the further research are presented at last.