American Institute of Mathematical Sciences

Advanced
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

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
[1]

Liuyang Yuan, Zhongping Wan, Qiuhua Tang. A criterion for an approximation global optimal solution based on the filled functions. Journal of Industrial & Management Optimization, 2016, 12 (1) : 375-387. doi: 10.3934/jimo.2016.12.375
[2]

Yongjian Yang, Zhiyou Wu, Fusheng Bai. A filled function method for constrained nonlinear integer programming. Journal of Industrial & Management Optimization, 2008, 4 (2) : 353-362. doi: 10.3934/jimo.2008.4.353
[3]

Xiaoqiang Dai, Wenke Li. Non-global solution for visco-elastic dynamical system with nonlinear source term in control problem. Electronic Research Archive, 2021, 29 (6) : 4087-4098. doi: 10.3934/era.2021073
[4]

Shaoyong Lai, Yong Hong Wu, Xu Yang. The global solution of an initial boundary value problem for the damped Boussinesq equation. Communications on Pure & Applied Analysis, 2004, 3 (2) : 319-328. doi: 10.3934/cpaa.2004.3.319
[5]

Wen-ling Zhao, Dao-jin Song. A global error bound via the SQP method for constrained optimization problem. Journal of Industrial & Management Optimization, 2007, 3 (4) : 775-781. doi: 10.3934/jimo.2007.3.775
[6]

Hirotada Honda. Global-in-time solution and stability of Kuramoto-Sakaguchi equation under non-local Coupling. Networks & Heterogeneous Media, 2017, 12 (1) : 25-57. doi: 10.3934/nhm.2017002
[7]

Lihuai Du, Ting Zhang. Local and global strong solution to the stochastic 3-D incompressible anisotropic Navier-Stokes equations. Discrete & Continuous Dynamical Systems, 2018, 38 (9) : 4745-4765. doi: 10.3934/dcds.2018209
[8]

Christos V. Nikolopoulos, Georgios E. Zouraris. Numerical solution of a non-local elliptic problem modeling a thermistor with a finite element and a finite volume method. Conference Publications, 2007, 2007 (Special) : 768-778. doi: 10.3934/proc.2007.2007.768
[9]

Jing Li, Boling Guo, Lan Zeng, Yitong Pei. Global weak solution and smooth solution of the periodic initial value problem for the generalized Landau-Lifshitz-Bloch equation in high dimensions. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1345-1360. doi: 10.3934/dcdsb.2019230
[10]

Deqiang Qu, Youlin Shang, Dan Wu, Guanglei Sun. Filled function method to optimize supply chain transportation costs. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021115
[11]

Mengmeng Zheng, Ying Zhang, Zheng-Hai Huang. Global error bounds for the tensor complementarity problem with a P-tensor. Journal of Industrial & Management Optimization, 2019, 15 (2) : 933-946. doi: 10.3934/jimo.2018078
[12]

Feng Li, Yuxiang Li. Global existence of weak solution in a chemotaxis-fluid system with nonlinear diffusion and rotational flux. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5409-5436. doi: 10.3934/dcdsb.2019064
[13]

Xiaoyun Cai, Liangwen Liao, Yongzhong Sun. Global strong solution to the initial-boundary value problem of a 2-D Kazhikhov-Smagulov type model. Discrete & Continuous Dynamical Systems - S, 2014, 7 (5) : 917-923. doi: 10.3934/dcdss.2014.7.917
[14]

Zhenhua Guo, Zilai Li. Global existence of weak solution to the free boundary problem for compressible Navier-Stokes. Kinetic & Related Models, 2016, 9 (1) : 75-103. doi: 10.3934/krm.2016.9.75
[15]

Peng Jiang. Unique global solution of an initial-boundary value problem to a diffusion approximation model in radiation hydrodynamics. Discrete & Continuous Dynamical Systems, 2015, 35 (7) : 3015-3037. doi: 10.3934/dcds.2015.35.3015
[16]

Chien-Wen Chao, Shu-Cherng Fang, Ching-Jong Liao. A tropical cyclone-based method for global optimization. Journal of Industrial & Management Optimization, 2012, 8 (1) : 103-115. doi: 10.3934/jimo.2012.8.103
[17]

Li-Fang Dai, Mao-Lin Liang, Wei-Yuan Ma. Optimization problems on the rank of the solution to left and right inverse eigenvalue problem. Journal of Industrial & Management Optimization, 2015, 11 (1) : 171-183. doi: 10.3934/jimo.2015.11.171
[18]

Yu-Lin Chang, Jein-Shan Chen, Jia Wu. Proximal point algorithm for nonlinear complementarity problem based on the generalized Fischer-Burmeister merit function. Journal of Industrial & Management Optimization, 2013, 9 (1) : 153-169. doi: 10.3934/jimo.2013.9.153
[19]

Rentsen Enkhbat, Evgeniya A. Finkelstein, Anton S. Anikin, Alexandr Yu. Gornov. Global optimization reduction of generalized Malfatti's problem. Numerical Algebra, Control & Optimization, 2017, 7 (2) : 211-221. doi: 10.3934/naco.2017015
[20]

Jin Feng He, Wei Xu, Zhi Guo Feng, Xinsong Yang. On the global optimal solution for linear quadratic problems of switched system. Journal of Industrial & Management Optimization, 2019, 15 (2) : 817-832. doi: 10.3934/jimo.2018072

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (62)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy