Convergent conditions of the generalized Newton method for absolute value equation over second order cones

2019 ◽  
Vol 92 ◽  
pp. 151-157 ◽  
Author(s):  
Baohua Huang ◽  
Changfeng Ma
Keyword(s):  
Newton Method ◽  
Second Order ◽  
Generalized Newton Method ◽  
Absolute Value Equation ◽  
Absolute Value ◽  
Generalized Newton

scholarly journals A Two-Step Newton-Type Method for Solving System of Absolute Value Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Lei Shi ◽  
Javed Iqbal ◽  
Muhammad Arif ◽  
Alamgir Khan
Keyword(s):  
Newton Method ◽  
New Method ◽  
Generalized Newton Method ◽  
Absolute Value Equations ◽  
Step Method ◽  
Type Method ◽  
Numerical Examples ◽  
Absolute Value ◽  
Generalized Newton

In this paper, we suggest a Newton-type method for solving the system of absolute value equations. This new method is a two-step method with the generalized Newton method as predictor. Convergence of the proposed method is proved under some suitable conditions. At the end, we take several numerical examples to show that the new method is very effective.

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.

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