scholarly journals An Interval Matrix Based Generalized Newton Method for Linear Complementarity Problems

2015 ◽  
Vol 05 (08) ◽  
pp. 443-449 ◽  
Author(s):  
Hai-Shan Han ◽  
Lan-Ying  
Keyword(s):  
Newton Method ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Generalized Newton Method ◽  
Interval Matrix ◽  
Generalized Newton

scholarly journals A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yuan Li ◽  
Hai-Shan Han ◽  
Dan-Dan Yang
Keyword(s):  
Newton Method ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Singular Values ◽  
Linear Complementarity ◽  
Positive Definite ◽  
Generalized Newton Method ◽  
Absolute Value ◽  
The Matrix ◽  
Generalized Newton

We consider a class of absolute-value linear complementarity problems. We propose a new approximation reformulation of absolute value linear complementarity problems by using a nonlinear penalized equation. Based on this approximation reformulation, a penalized-equation-based generalized Newton method is proposed for solving the absolute value linear complementary problem. We show that the proposed method is globally and superlinearly convergent when the matrix of complementarity problems is positive definite and its singular values exceed 1. Numerical results show that our proposed method is very effective and efficient.

A globally convergent damped Gauss–Newton method for solving the extended linear complementarity problem

2015 ◽  
Vol 23 (3) ◽  
Author(s):  
Na Huang ◽  
Changfeng Ma
Keyword(s):  
Newton Method ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Optimization Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
System Of Equations ◽  
Extended Linear Complementarity Problem ◽  
Special Cases

AbstractThe extended linear complementarity problem (denoted by XLCP), of which the linear and horizontal linear complementarity problems are two special cases, can be reformulated as the solution of a nonsmooth system of equations. By the symmetrically perturbed smoothing Fischer-Burmeister function, the XLCP is approximated by a family of parameterized smoothness optimization problems. Asmoothing damped Gauss-Newton method is designed for solving the XLCP. The proposed algorithm is proved to be convergent globally under suitable assumptions. Some numerical results are reported in the paper

Sign in / Sign up

Export Citation Format

Share Document