A smoothing Levenberg-Marquardt method for the complementarity problem over symmetric cone

2021 ◽  
pp. 1-16
Author(s):  
Xiangjing Liu ◽  
Sanyang Liu
Keyword(s):  
Complementarity Problem ◽  
Symmetric Cone ◽  
Marquardt Method ◽  
Levenberg Marquardt

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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