Discontinuous penalty approach with deviation integral for global constrained minimization

doi:10.1007/s10483-009-0915-x

Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (9): 1201-1210.doi: https://doi.org/10.1007/s10483-009-0915-x

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Discontinuous penalty approach with deviation integral for global constrained minimization

陈柳¹ 姚奕荣¹ 郑权^1,2

1. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;
2. Department of Mathematics, Columbus State University, Columbus, GA 31907, USA

收稿日期:2009-03-06 修回日期:2009-06-27 出版日期:2009-09-01 发布日期:2009-09-01

Discontinuous penalty approach with deviation integral for global constrained minimization

CHEN Liu¹, TAO Yi-Rong¹, ZHENG Quan^1,2

1. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;
2. Department of Mathematics, Columbus State University, Columbus, GA 31907, USA

Received:2009-03-06 Revised:2009-06-27 Online:2009-09-01 Published:2009-09-01

摘要/Abstract

摘要： In this paper, we use the discontinuous exact penalty functions to solve the constrained minimization problems with an integral approach. We examine a general form of the constrained deviation integral and its analytical properties. The optimality conditions of the penalized minimization problems are proven. To implement the algorithm, the cross-entropy method and the importance sampling are used based on the Monte-Carlo technique. Numerical tests show the effectiveness of the proposed algorithm.

关键词: global optimization, constrained problems, deviation integral, cross-entropy method

Abstract: In this paper, we use the discontinuous exact penalty functions to solve the constrained minimization problems with an integral approach. We examine a general form of the constrained deviation integral and its analytical properties. The optimality conditions of the penalized minimization problems are proven. To implement the algorithm, the cross-entropy method and the importance sampling are used based on the Monte-Carlo technique. Numerical tests show the effectiveness of the proposed algorithm.

Key words: global optimization, constrained problems, deviation integral, cross-entropy method

中图分类号:

陈柳姚奕荣郑权. Discontinuous penalty approach with deviation integral for global constrained minimization[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(9): 1201-1210.

CHEN Liu;TAO Yi-Rong;ZHENG Quan. Discontinuous penalty approach with deviation integral for global constrained minimization[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(9): 1201-1210.

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Discontinuous penalty approach with deviation integral for global constrained minimization

Discontinuous penalty approach with deviation integral for global constrained minimization

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