Verification of Iterative Methods for the Linear Complementarity Problem: Verification of Iterative Methods for LCPs

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Author(s): H. Saberi Najafi (Islamic Azad University, Lahijan Branch, Iran)and S. A. Edalatpanah (Islamic Azad University, Lahijan Branch, Iran)
Copyright: 2016
Pages: 36
Source title: Handbook of Research on Modern Optimization Algorithms and Applications in Engineering and Economics
Source Author(s)/Editor(s): Pandian Vasant (University of Technology Petronas, Malaysia), Gerhard-Wilhelm Weber (Middle East Technical University, Turkey)and Vo Ngoc Dieu (Ho Chi Minh City University of Technology, Vietnam)
DOI: 10.4018/978-1-4666-9644-0.ch021

Keywords: Algorithms / Artificial Intelligence / Computer Science & IT / Information Science Reference

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Abstract

In the present chapter, we give an overview of iterative methods for linear complementarity problems (abbreviated as LCPs). We also introduce these iterative methods for the problems based on fixed-point principle. Next, we present some new properties of preconditioned iterative methods for solving the LCPs. Convergence results of the sequence generated by these methods and also the comparison analysis between classic Gauss-Seidel method and preconditioned Gauss-Seidel (PGS) method for LCPs are established under certain conditions. Finally, the efficiency of these methods is demonstrated by numerical experiments. These results show that the mentioned models are effective in actual implementation and competitive with each other.

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Verification of Iterative Methods for the Linear Complementarity Problem: Verification of Iterative Methods for LCPs

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