基于不等式约束的一类新的增广Lagrangian函数  

A New Augmented Lagrangian Function Based on Inequalty Constraints Problem

作　　者：刘牧华[1] 尚有林[1] 李璞[1] 

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471003

出　　处：《运筹学学报》2011年第4期115-123,共9页Operations Research Transactions

基　　金：国家自然科学基金(10971053;10771162);河南省自然科学基金(094300510050)

摘　　要：针对含不等式约束的非线性规划问题,提出了一类新的增广Lagrangian函数,证明了其稳定点、整体极小点与原约束问题KKT点、整体极小点有对应关系,增广Lagrangian函数的局部极小点为原问题的局部极小点.基于给出的新的增广Lagrangian函数进行了数值计算,验证了其可行性和有效性.A new kind of augmented Lagrangian functions is proposed in this paper. We proved that there are the 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.Calculation examples show that the augmented Lagrangian function is feasible and effctive.

关 键 词：局部极小点 整体极小点 增广Lagrangian函数 KKT点 

分 类 号：O223[理学—运筹学与控制论]