July  2009, 5(3): 585-601. doi: 10.3934/jimo.2009.5.585

A penalty function algorithm with objective parameters for nonlinear mathematical programming

1. 

College of Business and Administration, Zhejiang University of Technology, Zhejiang 310023, China

2. 

School of Management, Fudan University, Shanghai 200433

3. 

Department of Manufacturing Engineering & Engineering Management, City University of Hong Kong, Kowloon, Hong Kong, China

Received  June 2008 Revised  November 2008 Published  June 2009

In this paper, we present a penalty function with objective parameters for inequality constrained optimization problems. We prove that this type of penalty functions has good properties for helping to solve inequality constrained optimization problems. Moreover, based on the penalty function, we develop an algorithm to solve the inequality constrained optimization problems and prove its convergence under some conditions. Numerical experiments show that we can obtain a satisfactorily approximate solution for some constrained optimization problems as the same as the exact penalty function.
Citation: Zhiqing Meng, Qiying Hu, Chuangyin Dang. A penalty function algorithm with objective parameters for nonlinear mathematical programming. Journal of Industrial and Management Optimization, 2009, 5 (3) : 585-601. doi: 10.3934/jimo.2009.5.585
[1]

Cheng Ma, Xun Li, Ka-Fai Cedric Yiu, Yongjian Yang, Liansheng Zhang. On an exact penalty function method for semi-infinite programming problems. Journal of Industrial and Management Optimization, 2012, 8 (3) : 705-726. doi: 10.3934/jimo.2012.8.705

[2]

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

[3]

Bao Qing Hu, Song Wang. A novel approach in uncertain programming part II: a class of constrained nonlinear programming problems with interval objective functions. Journal of Industrial and Management Optimization, 2006, 2 (4) : 373-385. doi: 10.3934/jimo.2006.2.373

[4]

Hassen Aydi, Ayman Kachmar. Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint. II. Communications on Pure and Applied Analysis, 2009, 8 (3) : 977-998. doi: 10.3934/cpaa.2009.8.977

[5]

Regina S. Burachik, C. Yalçın Kaya. An update rule and a convergence result for a penalty function method. Journal of Industrial and Management Optimization, 2007, 3 (2) : 381-398. doi: 10.3934/jimo.2007.3.381

[6]

Tone-Yau Huang, Tamaki Tanaka. Optimality and duality for complex multi-objective programming. Numerical Algebra, Control and Optimization, 2022, 12 (1) : 121-134. doi: 10.3934/naco.2021055

[7]

Yang Li, Liwei Zhang. A nonlinear Lagrangian method based on Log-Sigmoid function for nonconvex semidefinite programming. Journal of Industrial and Management Optimization, 2009, 5 (3) : 651-669. doi: 10.3934/jimo.2009.5.651

[8]

Shiyun Wang, Yong-Jin Liu, Yong Jiang. A majorized penalty approach to inverse linear second order cone programming problems. Journal of Industrial and Management Optimization, 2014, 10 (3) : 965-976. doi: 10.3934/jimo.2014.10.965

[9]

Jiang-Xia Nan, Deng-Feng Li. Linear programming technique for solving interval-valued constraint matrix games. Journal of Industrial and Management Optimization, 2014, 10 (4) : 1059-1070. doi: 10.3934/jimo.2014.10.1059

[10]

Changjun Yu, Kok Lay Teo, Liansheng Zhang, Yanqin Bai. A new exact penalty function method for continuous inequality constrained optimization problems. Journal of Industrial and Management Optimization, 2010, 6 (4) : 895-910. doi: 10.3934/jimo.2010.6.895

[11]

Yanqin Bai, Chuanhao Guo. Doubly nonnegative relaxation method for solving multiple objective quadratic programming problems. Journal of Industrial and Management Optimization, 2014, 10 (2) : 543-556. doi: 10.3934/jimo.2014.10.543

[12]

Xin Sun, Dachuan Xu, Dongmei Zhang, Yang Zhou. An adaptive algorithm for maximization of non-submodular function with a matroid constraint. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022031

[13]

Yanting Huang, Zongjun Wang. Pricing decisions for closed-loop supply chains with technology licensing and carbon constraint under reward-penalty mechanism. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022103

[14]

Jiahui Tang, Yifan Xu, Wei Wang. An approach to solve local and global optimization problems based on exact objective filled penalty functions. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022084

[15]

Vladimir Gaitsgory, Tanya Tarnopolskaya. Threshold value of the penalty parameter in the minimization of $L_1$-penalized conditional value-at-risk. Journal of Industrial and Management Optimization, 2013, 9 (1) : 191-204. doi: 10.3934/jimo.2013.9.191

[16]

Harry L. Johnson, David Russell. Transfer function approach to output specification in certain linear distributed parameter systems. Conference Publications, 2003, 2003 (Special) : 449-458. doi: 10.3934/proc.2003.2003.449

[17]

Yibing Lv, Tiesong Hu, Jianlin Jiang. Penalty method-based equilibrium point approach for solving the linear bilevel multiobjective programming problem. Discrete and Continuous Dynamical Systems - S, 2020, 13 (6) : 1743-1755. doi: 10.3934/dcdss.2020102

[18]

Behrouz Kheirfam. Multi-parametric sensitivity analysis of the constraint matrix in piecewise linear fractional programming. Journal of Industrial and Management Optimization, 2010, 6 (2) : 347-361. doi: 10.3934/jimo.2010.6.347

[19]

Mahdi Karimi, Seyed Jafar Sadjadi. Optimization of a Multi-Item Inventory model for deteriorating items with capacity constraint using dynamic programming. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1145-1160. doi: 10.3934/jimo.2021013

[20]

Robert Baier, Lars Grüne, Sigurđur Freyr Hafstein. Linear programming based Lyapunov function computation for differential inclusions. Discrete and Continuous Dynamical Systems - B, 2012, 17 (1) : 33-56. doi: 10.3934/dcdsb.2012.17.33

2021 Impact Factor: 1.411

Metrics

  • PDF downloads (453)
  • HTML views (0)
  • Cited by (20)

Other articles
by authors

[Back to Top]