Sub-quadratic convergence of a smoothing Newton method for symmetric cone complementarity problems

2015 ◽  
Author(s):  
Yanling He ◽  
Chunyan Liu
Keyword(s):  
Newton Method ◽  
Quadratic Convergence ◽  
Complementarity Problems ◽  
Symmetric Cone ◽  
Smoothing Newton Method

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.

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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