A projection method for linear complementarity problems

In this article we present an iterative two-step algorithm for the numerical solution of linear complementarity problems(LCP). The algorithm presented combines the active set strategy with the square conjugated gradient method for the linear system solution. This interative two-step algorithm was based on a similar one developed by Kocvara & Zowe, that combines the symmetric successive over relaxation with projection method and the preconditioned conjugated gradient method. In the Numerical Experience section, we have tested the method for solve some LCP with non-singular matrices. Such matrices belong to semipositive definite matrix class, P-matrix class and P0-matrix class. Furthermore we show a comparison between our method and the one developed by Pardalos, Ye, Han & Kaliski.