American Institute of Mathematical Sciences

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

A penalty function algorithm with objective parameters for nonlinear mathematical programming

Zhiqing Meng 1, , Qiying Hu 2, and  Chuangyin Dang 3,

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.
Keywords: Nonlinear programming, constraint., objective parameter, penalty function.
Mathematics Subject Classification: Primary: 65K05; Secondary: 90C3.
Citation: Zhiqing Meng, Qiying Hu, Chuangyin Dang. A penalty function algorithm with objective parameters for nonlinear mathematical programming. Journal of Industrial & Management Optimization, 2009, 5 (3) : 585-601. doi: 10.3934/jimo.2009.5.585
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