Journal of Industrial and Management Optimization (JIMO)

A penalty function algorithm with objective parameters for nonlinear mathematical programming

Pages: 585 - 601, Volume 5, Issue 3, August 2009      doi:10.3934/jimo.2009.5.585

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Zhiqing Meng - College of Business and Administration, Zhejiang University of Technology, Zhejiang 310023, China (email)
Qiying Hu - School of Management, Fudan University, Shanghai 200433, China (email)
Chuangyin Dang - Department of Manufacturing Engineering & Engineering Management, City University of Hong Kong, Kowloon, Hong Kong, China (email)

Abstract: 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, penalty function, objective parameter, constraint.
Mathematics Subject Classification:  Primary: 65K05; Secondary: 90C30.

Received: June 2008;      Revised: November 2008;      Available Online: June 2009.