The quadratic convergence of a smoothing Levenberg–Marquardt method for nonlinear complementarity problem

2008 ◽  
Vol 197 (2) ◽  
pp. 566-581 ◽  
Author(s):  
Changfeng Ma ◽  
Jia Tang
Keyword(s):  
Complementarity Problem ◽  
Quadratic Convergence ◽  
Nonlinear Complementarity Problem ◽  
Nonlinear Complementarity ◽  
Marquardt Method ◽  
Levenberg Marquardt

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.

scholarly journals Levenberg-Marquardt Method for the Eigenvalue Complementarity Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yuan-yuan Chen ◽  
Yan Gao
Keyword(s):  
Complementarity Problem ◽  
Numerical Experiments ◽  
Nonlinear Complementarity Problem ◽  
Mathematical Programming Problem ◽  
Complementarity Constraints ◽  
Marquardt Method ◽  
Globally Convergent ◽  
Eigenvalue Complementarity Problem ◽  
Semismooth Newton ◽  
Levenberg Marquardt

The eigenvalue complementarity problem (EiCP) is a kind of very useful model, which is widely used in the study of many problems in mechanics, engineering, and economics. The EiCP was shown to be equivalent to a special nonlinear complementarity problem or a mathematical programming problem with complementarity constraints. The existing methods for solving the EiCP are all nonsmooth methods, including nonsmooth or semismooth Newton type methods. In this paper, we reformulate the EiCP as a system of continuously differentiable equations and give the Levenberg-Marquardt method to solve them. Under mild assumptions, the method is proved globally convergent. Finally, some numerical results and the extensions of the method are also given. The numerical experiments highlight the efficiency of the method.

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