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.

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.

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 Newton method for nonlinear complementarity problems

2013 ◽  
Vol 32 (1) ◽  
pp. 107-118 ◽  
Author(s):  
Jingyong Tang ◽  
Li Dong ◽  
Jinchuan Zhou ◽  
Liang Fang
Keyword(s):  
Newton Method ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problems ◽  
Smoothing Newton Method ◽  
Nonlinear Complementarity

scholarly journals Long step homogeneous interior point algorithm for the p* nonlinear complementarity problems

2002 ◽  
Vol 12 (1) ◽  
pp. 17-48
Author(s):  
Goran Lesaja
Keyword(s):  
Global Convergence ◽  
Linear Complementarity Problem ◽  
Interior Point ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problem ◽  
Linear Complementarity ◽  
Compact Set ◽  
Interior Point Algorithm ◽  
Nonlinear Complementarity

A P*-Nonlinear Complementarity Problem as a generalization of the P*-Linear Complementarity Problem is considered. We show that the long-step version of the homogeneous self-dual interior-point algorithm could be used to solve such a problem. The algorithm achieves linear global convergence and quadratic local convergence under the following assumptions: the function satisfies a modified scaled Lipschitz condition, the problem has a strictly complementary solution, and certain submatrix of the Jacobian is nonsingular on some compact set.

scholarly journals A new smoothing method for solving nonlinear complementarity problems

2019 ◽  
Vol 17 (1) ◽  
pp. 104-119 ◽  
Author(s):  
Jianguang Zhu ◽  
Binbin Hao
Keyword(s):  
Newton Method ◽  
Quadratic Convergence ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problem ◽  
Smoothing Newton Method ◽  
Convergence Properties ◽  
Linear System Of Equations ◽  
Complementarity Conditions ◽  
Nonlinear Complementarity ◽  
Global And Local

Abstract In this paper, a new improved smoothing Newton algorithm for the nonlinear complementarity problem was proposed. This method has two-fold advantages. First, compared with the classical smoothing Newton method, our proposed method needn’t nonsingular of the smoothing approximation function; second, the method also inherits the advantage of the classical smoothing Newton method, it only needs to solve one linear system of equations at each iteration. Without the need of strict complementarity conditions and the assumption of P0 property, we get the global and local quadratic convergence properties of the proposed method. Numerical experiments show that the efficiency of the proposed method.

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