Solution of nonsymmetric linear complementarity problems by iterative methods

Abstract

Convergence is established for iterative algorithms for the solution of the nonsymmetric linear complementarity problem of findingz such thatMz+q⩾0,z⩾0,zT(Mz+q)=0, whereM is a givenn×n real matrix, not necessarily symmeetric, andq is a givenn-vector. It is first shown that, if the spectral radius of a matrix related toM is less than one, then the iterates generated by the general algorithm converge to a solution of the linear complementarity problem. It turns out that convergence properties are quite similar to those of linear systems of equations. As specific cases, two important classes of matrices, Minkowski matrices and quasi-dominant diagonal matrices, are shown to satisfy this convergence condition.