The Existence Of Solution For Lcp(M,q) And Related-Matrices

The linear complementarity problem is very useful in economics, game theory and mathematical programming .The classical linear programming and quadratic programming all can transform to the linear complementarity problem. The Lemke method is one of the most regularity methods to solve the linear complementarity problem. The existence of solution for the linear complementarity problem is related with special matrices. In this paper we introduce the proper- C0 ? martrix and proper- semi positive definite matrix .Then we study the relations of these special matrices and also give some new theories about the existence of solution .We further more research the condition of special matrix being semi positive definite matrix and partly solve the sufficient conditions of Murthy guesses. For methods, we first give a iterative algorithm and prove the convergence. Lemke method is one famous method of the linear complementarity problem, this paper gives the improving of Lemke method for some matrices that are not C ? matrices .