基于不等式约束的一类新的增广lagrangian函数

运筹学学报 ›› 2011, Vol. 15 ›› Issue (4): 115-123.

基于不等式约束的一类新的增广lagrangian函数

刘牧华, 尚有林, 李璞

1. 河南科技大学数学与统计学院
2. 河南科技大学

收稿日期:2011-04-02 修回日期:2011-05-31 出版日期:2011-12-15 发布日期:2011-12-19
通讯作者: 刘牧华 E-mail:lxk0379@126.com

A new augmented lagrangian function based on inequalty constraints problem

LIU Mu-Hua, SHANG You-Lin, LI Pu

Received:2011-04-02 Revised:2011-05-31 Online:2011-12-15 Published:2011-12-19

摘要/Abstract

摘要： 本文提出了一类新的增广lagrangian函数，并证明了它的稳定点、整体极小点与原约束问题KKT点、整体极小点有1-1对应关系，增广lagrangian函数的局部极小点为原问题的局部极小点.

关键词: 局部极小点, 整体极小点, 增广Lagrangian函数, KKT点

Abstract: A new kind of augmented lagrangian function is proposed in this paper. We proved that there are the 1-1 corresponding relationships between the stable point of the lagrangian function and KKT point of the original problem. The same results are obtained for the both global minimum point. The local minimum point of the augmented lagrangian function is the local minimum point of the original problem.

Key words: local minimum point, global minimum point, augmented
Lagrangian function, KKT point

刘牧华, 尚有林, 李璞. 基于不等式约束的一类新的增广lagrangian函数[J]. 运筹学学报, 2011, 15(4): 115-123.

LIU Mu-Hua, SHANG You-Lin, LI Pu. A new augmented lagrangian function based on inequalty constraints problem[J]. Operations Research Transactions, 2011, 15(4): 115-123.

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