A generalized Newton method for non-Hermitian positive definite linear complementarity problem

CALCOLO ◽  
2016 ◽  
Vol 54 (1) ◽  
pp. 43-56 ◽  
Author(s):  
Shi-Liang Wu ◽  
Cui-Xia Li
Keyword(s):  
Newton Method ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Positive Definite ◽  
Generalized Newton Method ◽  
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

scholarly journals Generalized Newton Method for a Kind of Complementarity Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Shou-qiang Du
Keyword(s):  
Global Convergence ◽  
Newton Method ◽  
Differentiable Function ◽  
Local Convergence ◽  
Complementarity Problem ◽  
Merit Function ◽  
Nonsmooth Equations ◽  
Generalized Newton Method ◽  
Convergence Results ◽  
Generalized Newton

A generalized Newton method for the solution of a kind of complementarity problem is given. The method is based on a nonsmooth equations reformulation of the problem byF-Bfunction and on a generalized Newton method. The merit function used is a differentiable function. The global convergence and superlinear local convergence results are also given under suitable assumptions. Finally, some numerical results and discussions are presented.

scholarly journals Generalized SOR-Like Iteration Method for Linear Complementarity Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Cui-Xia Li ◽  
Shi-Liang Wu
Keyword(s):  
Fixed Point ◽  
Linear Complementarity Problem ◽  
Iteration Method ◽  
Complementarity Problem ◽  
Numerical Experiments ◽  
Linear Complementarity ◽  
Positive Definite ◽  
Convergence Properties ◽  
Fixed Point Equation ◽  
Point Equation

In this paper, we present a generalized SOR-like iteration method to solve the non-Hermitian positive definite linear complementarity problem (LCP), which is obtained by reformulating equivalently the implicit fixed-point equation of the LCP as a two-by-two block nonlinear equation. The convergence properties of the generalized SOR-like iteration method are discussed under certain conditions. Numerical experiments show that the generalized SOR-like method is efficient, compared with the SOR-like method and the modulus-based SOR method.

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