Predictor-Corrector Smoothing Newton Method, Based on a New Smoothing Function, for Solving the Nonlinear Complementarity Problem with a P 0 Function

2003 ◽  
Vol 117 (1) ◽  
pp. 39-68 ◽  
Author(s):  
Z.H. Huang ◽  
J. Han ◽  
Z. Chen
Keyword(s):  
Newton Method ◽  
Complementarity Problem ◽  
Nonlinear Complementarity Problem ◽  
Smoothing Newton Method ◽  
Smoothing Function ◽  
Nonlinear Complementarity ◽  
Predictor Corrector

A Smoothing Newton Method for Nonlinear Complementarity Problems

2013 ◽  
Vol 475-476 ◽  
pp. 1090-1093
Author(s):  
Ning Feng ◽  
Zhi Yuan Tian ◽  
Xin Lei Qu
Keyword(s):  
Global Convergence ◽  
Numerical Experiment ◽  
Newton Method ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problem ◽  
Nonlinear Complementarity Problems ◽  
Smoothing Newton Method ◽  
Nonlinear Complementarity ◽  
Mild Conditions

A new FB-function based on the P0 function is given in this paper. The nonlinear complementarity problem is reformulated to solve equivalent equations based on the FB-function. A modified smooth Newton method is proposed for nonlinear complementarity problem. Under mild conditions, the global convergence of the algorithm is proved. The numerical experiment shows that the algorithm is potentially efficient.

scholarly journals A Double Nonmonotone Quasi-Newton Method for Nonlinear Complementarity Problem Based on Piecewise NCP Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhensheng Yu ◽  
Zilun Wang ◽  
Ke Su
Keyword(s):  
Global Convergence ◽  
Newton Method ◽  
Complementarity Problem ◽  
Line Search ◽  
Nonlinear Complementarity Problem ◽  
Practical Applications ◽  
Nonlinear Complementarity ◽  
Complementarity Functions ◽  
Single Solution ◽  
Quasi Newton

In this paper, a double nonmonotone quasi-Newton method is proposed for the nonlinear complementarity problem. By using 3-1 piecewise and 4-1 piecewise nonlinear complementarity functions, the nonlinear complementarity problem is reformulated into a smooth equation. By a double nonmonotone line search, a smooth Broyden-like algorithm is proposed, where a single solution of a smooth equation at each iteration is required with the reduction in the scale of the calculation. Under suitable conditions, the global convergence of the algorithm is proved, and numerical results with some practical applications are given to show the efficiency of the algorithm.

scholarly journals A Smoothing Inexact Newton Method for Generalized Nonlinear Complementarity Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Meixia Li ◽  
Haitao Che
Keyword(s):  
Complementarity Problem ◽  
Line Search ◽  
Quadratic Convergence ◽  
Nonlinear Complementarity Problem ◽  
Accumulation Point ◽  
Smoothing Function ◽  
Inexact Newton Method ◽  
Nonlinear Complementarity ◽  
Ncp Function ◽  
Independent Variable

Based on the smoothing function of penalized Fischer-Burmeister NCP-function, we propose a new smoothing inexact Newton algorithm with non-monotone line search for solving the generalized nonlinear complementarity problem. We view the smoothing parameter as an independent variable. Under suitable conditions, we show that any accumulation point of the generated sequence is a solution of the generalized nonlinear complementarity problem. We also establish the local superlinear (quadratic) convergence of the proposed algorithm under the BD-regular assumption. Preliminary numerical experiments indicate the feasibility and efficiency of the proposed algorithm.

Sign in / Sign up

Export Citation Format

Share Document