# American Institute of Mathematical Sciences

October  2009, 5(4): 911-928. doi: 10.3934/jimo.2009.5.911

## A filled function method for solving nonlinear complementarity problem

 1 School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China, China 2 School of Mathematics and Statistics, Wuhan University, Wuhan, MO 430072, China, China

Received  May 2008 Revised  July 2009 Published  August 2009

In this paper a filled function method is suggested for solving the nonlinear complementarity problem. Firstly, the original problem is converted into a corresponding unconstrained optimization problem by using the Fischer-Burmeister function. Subsequently, a new filled function with one parameter is proposed for solving unconstrained optimization problems. Some properties of the filled function are studied and discussed without Lipschitz continuity condition. Finally, an algorithm based on the proposed filled function for solving the nonlinear complementarity problem is presented. The implementation of the algorithm on several test problems is reported with numerical results.
Citation: Liuyang Yuan, Zhongping Wan, Jingjing Zhang, Bin Sun. A filled function method for solving nonlinear complementarity problem. Journal of Industrial and Management Optimization, 2009, 5 (4) : 911-928. doi: 10.3934/jimo.2009.5.911
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