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October 2010, 6(4): 895-910. doi: 10.3934/jimo.2010.6.895
A new exact penalty function method for continuous inequality constrained optimization problems
Changjun Yu 1, , Kok Lay Teo 1, , Liansheng Zhang 2, and Yanqin Bai 2,
Department of Mathematics and Statistics, Curtin University of Technology, Kent Street, Bentley 6102, WA, Australia, Australia
Department of Mathematics, Shanghai University, 99, Shangda Road, 200444, Shanghai, China, China
Received March 2010 Revised July 2010 Published September 2010
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, Constrained Optimization., Semi-Infinite Programming.
Mathematics Subject Classification: Primary: 90-08; Secondary: 90C34, 49M3.
Citation: Changjun Yu, Kok Lay Teo, Liansheng Zhang, Yanqin Bai. A new exact penalty function method for continuous inequality constrained optimization problems. Journal of Industrial & Management Optimization, 2010, 6 (4) : 895-910. doi: 10.3934/jimo.2010.6.895
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Changjun Yu Kok Lay Teo Liansheng Zhang Yanqin Bai