一类新的精确增广Lagrangian函数的性质

J4 ›› 2013, Vol. 48 ›› Issue (12): 90-95.

一类新的精确增广Lagrangian函数的性质

李梅霞1,2,刘茜3

1. 潍坊学院数学与信息科学学院, 山东潍坊 261061; 2. 北京工业大学应用数理学院, 北京 100022;
3.山东师范大学数学科学学院，山东济南 250014

收稿日期:2012-12-04 出版日期:2013-12-20 发布日期:2014-01-09
作者简介:李梅霞(1970- ),女，副教授，博士，研究方向为最优化理论与方法.Email: limeixia001@163.com一类新的精确增广Lagrangian函数的性质
基金资助:
北京市博士后工作经费资助项目(2012ZZ23);国家自然科学基金资助项目(10901096);山东省自然科学基金资助项目(ZR2009AL019);山东省高校科研发展计划项目(J09LA53)

Properties of a new kind of exact augmented Lagrangian function

LI Mei-xia1,2， LIU Qian3

1. School of Mathematics and Information Science, Weifang University, Weifang 261061, Shandong, China；
2. College of Applied Science, Beijing University of Technology, Beijing 100022, China;
3. School of Mathematics Science, Shandong Normal University, Jinan 250014, Shandong, China

Received:2012-12-04 Online:2013-12-20 Published:2014-01-09

摘要/Abstract

摘要：

针对含有等式和不等式混合约束的最优化问题引进了一种新的精确增广Lagrangian函数。证明了该类增广Lagrangian函数的基本性质。进一步, 在较弱的条件下证明了无约束问题的稳定点与原约束问题的KKT点之间的等价性。

关键词: 约束最优化;增广Lagrangian函数;性质

Abstract:

new kind of augmented Lagrangian function for constrained optimization problem with both equality and inequality contraints is introduced. The elementary properties of this kind of function are given. Furthermore, the equivalence between its slationary point of uncontrained minimization and the KKT point of the original constrained problem is proved.

Key words: constrained optimization; augmented Lagrangian function; property

中图分类号:

O221.2

李梅霞1,2,刘茜3. 一类新的精确增广Lagrangian函数的性质[J]. J4, 2013, 48(12): 90-95.

LI Mei-xia1,2， LIU Qian3. Properties of a new kind of exact augmented Lagrangian function[J]. J4, 2013, 48(12): 90-95.

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