New simple exact penalty function for constrained minimization

doi:10.1007/s10483-012-1597-x

Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (7): 951-962.doi: https://doi.org/10.1007/s10483-012-1597-x

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New simple exact penalty function for constrained minimization

郑芳英^1,2, 张连生²

1. Department of Mathematical Sciences, Zhejiang Sci-Tech University, Hangzhou 310018, P. R. China;
2. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China

收稿日期:2011-04-18 修回日期:2012-03-22 出版日期:2012-07-10 发布日期:2012-07-10
通讯作者: Fang-ying ZHENG, Ph.D., E-mail: fangyingzh@shu.edu.cn E-mail:fangyingzh@shu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 10571116 and 51075421)

New simple exact penalty function for constrained minimization

Fang-ying ZHENG^1,2, Lian-sheng ZHANG²

1. Department of Mathematical Sciences, Zhejiang Sci-Tech University, Hangzhou 310018, P. R. China;
2. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China

Received:2011-04-18 Revised:2012-03-22 Online:2012-07-10 Published:2012-07-10
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 10571116 and 51075421)

摘要/Abstract

摘要： By adding one variable to the equality-or inequality-constrained minimization problems, a new simple penalty function is proposed. It is proved to be exact in the sense that under mild assumptions, the local minimizers of this penalty function are precisely the local minimizers of the original problem, when the penalty parameter is sufficiently large.

关键词: nonlinear control system, controllability, oriented manifold, invariant manifold, basic system, dynamics of rigid body, nonlinear programming, constrained minimization, local solution, exact penalty function

Abstract: By adding one variable to the equality-or inequality-constrained minimization problems, a new simple penalty function is proposed. It is proved to be exact in the sense that under mild assumptions, the local minimizers of this penalty function are precisely the local minimizers of the original problem, when the penalty parameter is sufficiently large.

Key words: nonlinear control system, controllability, oriented manifold, invariant manifold, basic system, dynamics of rigid body, nonlinear programming, constrained minimization, local solution, exact penalty function

中图分类号:

O221.2

郑芳英;张连生. New simple exact penalty function for constrained minimization[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(7): 951-962.

Fang-ying ZHENG;Lian-sheng ZHANG. New simple exact penalty function for constrained minimization[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(7): 951-962.

参考文献

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New simple exact penalty function for constrained minimization

New simple exact penalty function for constrained minimization

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