A filled function method for solving nonlinear complementarity problem

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

A filled function method for solving nonlinear complementarity problem

Liuyang Yuan ^1, , Zhongping Wan ^1, , Jingjing Zhang ^2, and Bin Sun ^2,

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

Abstract
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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.

Keywords: The nonlinear complementarity problem, Local solution, Global optimization, Filled function method, Global solution..

Mathematics Subject Classification: Primary: 90C30; Secondary: 90C3.

Citation: Liuyang Yuan, Zhongping Wan, Jingjing Zhang, Bin Sun. A filled function method for solving nonlinear complementarity problem. Journal of Industrial & Management Optimization, 2009, 5 (4) : 911-928. doi: 10.3934/jimo.2009.5.911

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