Lcp Problem, Theoretical Analysis And Research

This paper is concerned with the solutions to linear complementarity problem and some classes of important matrices: P -matrix, H -marix, M -matrix. Because of the characters of itself, it is very important to study the solutions to linear complementarity problem. In this paper, we study the local uniqueness of the solutions to the extended linear complementarity problem (ELCP) by means of a concept which is an extension of the nondegenerate matrix in the standerd LCP. The ELCP contains as special cases the vertical linear complementarity problem (VLCP), horizontal linear complementarity problem (HLCP), the paper is devoted to find the characterization of the solutions to vertical linear complementarity problem and horizontal linear complementarity problem.Using the column (row) nondegeneracy (ND property)of {M , N } with respect to X ( X := { Lw + q / w≥0, w∈Rl},L∈R q∈Rm×l, ) characterizing the local uniqueness of the solutions to vertical linear complementarity problem (VLCP), horizontal linear complementarity problem (HLCP), we obtain two new results for the solutions to the extended linear complementarity problem, we also obtain the nondegeneracy of the matrix characterizing the Q H -column -property and -column -property to the pair {M , N }.