`a`
Journal of Industrial and Management Optimization (JIMO)
 

A new exact penalty function method for continuous inequality constrained optimization problems

Pages: 895 - 910, Volume 6, Issue 4, November 2010      doi:10.3934/jimo.2010.6.895

 
       Abstract        References        Full Text (211.0K)       Related Articles       

Changjun Yu - Department of Mathematics and Statistics, Curtin University of Technology, Kent Street, Bentley 6102, WA, Australia (email)
Kok Lay Teo - Department of Mathematics and Statistics, Curtin University of Technology, Kent Street, Bentley 6102, WA, Australia (email)
Liansheng Zhang - Department of Mathematics, Shanghai University, 99, Shangda Road, 200444, Shanghai, China (email)
Yanqin Bai - Department of Mathematics, Shanghai University, 99, Shangda Road, 200444, Shanghai, China (email)

Abstract: In this paper, a computational approach based on a new exact penalty function method is devised for solving a class of continuous inequality constrained optimization problems. The continuous inequality constraints are first approximated by smooth function in integral form. Then, we construct a new exact penalty function, where the summation of all these approximate smooth functions in integral form, called the constraint violation, is appended to the objective function. In this way, we obtain a sequence of approximate unconstrained optimization problems. It is shown that if the value of the penalty parameter is sufficiently large, then any local minimizer of the corresponding unconstrained optimization problem is a local minimizer of the original problem. For illustration, three examples are solved using the proposed method. From the solutions obtained, we observe that the values of their objective functions are amongst the smallest when compared with those obtained by other existing methods available in the literature. More importantly, our method finds solution which satisfies the continuous inequality constraints.

Keywords:  Exact Penalty Function, Semi-Infinite Programming, Constrained Optimization.
Mathematics Subject Classification:  Primary: 90-08; Secondary: 90C34, 49M37.

Received: March 2010;      Revised: July 2010;      Available Online: September 2010.

 References