On finite termination of an iterative method for linear complementarity problems

1996 ◽  
Vol 74 (3) ◽  
pp. 279-292 ◽  
Author(s):  
Andreas Fischer ◽  
Christian Kanzow
Keyword(s):  
Iterative Method ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Finite Termination

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 New error bounds for linear complementarity problems of Σ-SDD matrices and SB-matrices

2019 ◽  
Vol 17 (1) ◽  
pp. 1599-1614
Author(s):  
Zhiwu Hou ◽  
Xia Jing ◽  
Lei Gao
Keyword(s):  
Linear Algebra ◽  
Error Bound ◽  
Linear Complementarity Problem ◽  
Error Bounds ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Numerical Examples ◽  
Numer Algor ◽  
Better Than

Abstract A new error bound for the linear complementarity problem (LCP) of Σ-SDD matrices is given, which depends only on the entries of the involved matrices. Numerical examples are given to show that the new bound is better than that provided by García-Esnaola and Peña [Linear Algebra Appl., 2013, 438, 1339–1446] in some cases. Based on the obtained results, we also give an error bound for the LCP of SB-matrices. It is proved that the new bound is sharper than that provided by Dai et al. [Numer. Algor., 2012, 61, 121–139] under certain assumptions.

scholarly journals A notion of equivalence for linear complementarity problems Applications to the design of nonsmooth bifurcations

2020 ◽  
Vol 53 (2) ◽  
pp. 5435-5440
Author(s):  
Fernando Castaños ◽  
Felix A. Miranda-Villatoro ◽  
Alessio Franci
Keyword(s):  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity
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