A One-Step Smoothing Newton Method Based on a New Class of One-Parametric Nonlinear Complementarity Functions for P 0-NCP

2010 ◽  
pp. 110-117
Author(s):  
Liang Fang ◽  
Xianming Kong ◽  
Xiaoyan Ma ◽  
Han Li ◽  
Wei Zhang
Keyword(s):  
Newton Method ◽  
Smoothing Newton Method ◽  
Nonlinear Complementarity ◽  
New Class ◽  
Complementarity Functions ◽  
One Step

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.

A Smoothing Method for Solving the NCP Based on a New Smoothing Approximate Function

2013 ◽  
Vol 462-463 ◽  
pp. 294-297
Author(s):  
Wei Meng ◽  
Zhi Yuan Tian ◽  
Xin Lei Qu
Keyword(s):  
Global Convergence ◽  
Newton Method ◽  
Complementarity Problems ◽  
Numerical Results ◽  
Nonlinear Complementarity Problems ◽  
Smoothing Method ◽  
Smoothing Newton Method ◽  
Nonlinear Complementarity ◽  
Approximate Function

A new smoothing approximate function of the FischerBurmeister function is given. A modified smoothing Newton method based on the function is proposed for solving a kind of nonlinear complementarity problems. Under suitable conditions, the global convergence of the method is proved. Numerical results show the effectiveness of the method.

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