A generalized Newton method of high-order convergence for solving the large-scale linear complementarity problem

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

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An Entropy Interval Newton Method for Linear Complementarity Problem

2009 International Joint Conference on Computational Sciences and Optimization ◽

10.1109/cso.2009.308 ◽

2009 ◽

Author(s):

Yanqiang Wu ◽

Haiwen Xu

Keyword(s):

Newton Method ◽

Linear Complementarity Problem ◽

Complementarity Problem ◽

Linear Complementarity ◽

Interval Newton Method

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Generalized Newton Method for a Kind of Complementarity Problem

Abstract and Applied Analysis ◽

10.1155/2014/745981 ◽

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.

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

Journal of Mathematics ◽

10.1155/2014/560578 ◽

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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