Modification of iterative methods for solving linear complementarity problems

Abstract

Purpose – The purpose of this paper is to present the efficient iterative methods for solving linear complementarity problems (LCP), using a class of pre-conditioners. Design/methodology/approach – By using the concept of solving the fixed-point system of equations associated to the LCP, pre-conditioning techniques and Krylov subspace methods the authors design some projected methods to solve LCP. Furthermore, within the computational framework, some models of pre-conditioners candidates are investigated and evaluated. Findings – The proposed algorithms have a simple and graceful structure and can be applied to other complementarity problems. Asymptotic convergence of the sequence generated by the method to the unique solution of LCP is proved, along with a result regarding the convergence rate of the pre-conditioned methods. Finally, a computational comparison of the standard methods against pre-conditioned methods based on Example 1 is presented which illustrate the merits of simplicity, power and effectiveness of the proposed algorithms. Research limitations/implications – Comparison between the authors' methods and other similar methods for the studied problem shows a remarkable agreement and reveals that their models are superior in point of view rate of convergence and computing efficiency. Originality/value – For solving LCP more attention has recently been paid on a class of iterative methods called the matrix-splitting such as AOR, MAOR, GAOR, SSOR, etc. But up to now, no paper has discussed the effect of pre-conditioning technique for matrix-splitting methods in LCP. So, this paper is planning to fill in this gap and the authors use a class of pre-conditioners with iterative methods and analyze the convergence of these methods for LCP.