Approximate Augmented Lagrangian Functions and Nonlinear Semidefinite Programs

被引：0
|
作者：
X.X.HUANG [1 ]
K.L.TEO [2 ]
X.Q.YANG [3 ]
机构：
[1] School of Management, Fudan University, Shanghai 200433, P. R. China and Department of Mathematics and Computer Science, Chongqing Normal University,Chongqing 400047, P. R. China
[2] Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia
[3] Department of Applied Mathematics, The Hong Kong Polytechnic University,Kowloon, Hong Kong, P. R. China
来源：
Acta Mathematica Sinica,English Series | 2006年 / 22卷 / 05期
关键词：
semidefinite programming; augmented Lagrangian; duality; exact penalty; convergence; stationary point;
D O I：
暂无
中图分类号：
O174 [函数论]; O221.2 [非线性规划];
学科分类号：
070104 ; 070105 ; 1201 ;
摘要：
In this paper, an approximate augmented Lagrangian function for nonlinear semidefiniteprograms is introduced. Some basic properties of the approximate augmented Lagrange function suchas monotonicity and convexity are discussed. Necessary and sufficient conditions for approximatestrong duality results are derived. Conditions for an approximate exact penalty representation in theframework of augmented Lagrangian are given. Under certain conditions, it is shown that any limitpoint of a sequence of stationary points of approximate augmented Lagrangian problems is a KKT pointof the original semidefinite program and that a sequence of optimal solutions to augmented Lagrangianproblems converges to a solution of the original semidefinite program.
引用
收藏
页码：1283 / 1296
页数：14
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