On the preconditioned projective iterative methods for the linear complementarity problems

This paper aims to propose the new preconditioning approaches for solving linear complementarity problem (LCP). Some years ago, the preconditioned projected iterative methods were presented for the solution of the LCP, and the convergence of these methods has been analyzed. However, most of these methods are not correct, and this is because the complementarity condition of the preconditioned LCP is not always equivalent to that of the un-preconditioned original LCP. To overcome this shortcoming, we present a new strategy with a new preconditioner that ensures the solution of the same problem is correct. We also study the convergence properties of the new preconditioned iterative method for solving LCP. Finally, the new approach is illustrated with the help of a numerical example.