Global Convergence Properties of Some Iterative Methods for Linear Complementarity Problems

1996 ◽  
Vol 6 (2) ◽  
pp. 326-341 ◽  
Author(s):  
Christian Kanzow
Keyword(s):  
Global Convergence ◽  
Iterative Methods ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Convergence Properties

On the preconditioned projective iterative methods for the linear complementarity problems

2020 ◽  
Vol 54 (2) ◽  
pp. 341-349 ◽  
Author(s):  
Seyyed Ahmad Edalatpanah
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Convergence Properties ◽  
New Approach ◽  
Complementarity Condition ◽  
New Strategy ◽  
Preconditioned Iterative

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.

scholarly journals A Preconditioned Multisplitting and Schwarz Method for Linear Complementarity Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Cuiyu Liu ◽  
Chen-liang Li
Keyword(s):  
Convergence Rate ◽  
Iterative Methods ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Numerical Experiments ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Coefficient Matrix ◽  
Schwarz Method

The preconditioner presented by Hadjidimos et al. (2003) can improve on the convergence rate of the classical iterative methods to solve linear systems. In this paper, we extend this preconditioner to solve linear complementarity problems whose coefficient matrix isM-matrix orH-matrix and present a multisplitting and Schwarz method. The convergence theorems are given. The numerical experiments show that the methods are efficient.

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