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.
Keywords
Acknowledgements
The authors would like to thank Professor DRJ Owen, Editor of Engineering Computations for the valuable help and cooperations and also to thank the anonymous reviewers of this article for their great suggestions that improved this paper significantly.
Citation
Saberi Najafi, H. and Edalatpanah, S.A. (2013), "Modification of iterative methods for solving linear complementarity problems", Engineering Computations, Vol. 30 No. 7, pp. 910-923. https://doi.org/10.1108/EC-10-2011-0131
Publisher
:Emerald Group Publishing Limited
Copyright © 2013, Emerald Group Publishing Limited