半无限规划中的增广拉格朗日鞍点  

Saddle Points of Augmented Lagrangian for Semi-infinite Programming

作　　者：谷国利[1] 刘茜[1] 李敏[1] 

机构地区：[1]山东师范大学数学科学学院,济南250014

出　　处：《重庆师范大学学报（自然科学版）》2016年第6期8-12,共5页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11271226;No.11271233);山东省自然科学基金(No.ZR2013FL032);留学回国人员科研启动基金(No.教外司留[2015]1098)

摘　　要：考虑一类半无限规划问题,它是许多现实生活问题中数学模型的强力工具。采用一种增广拉格朗日方法来解决半无限规划问题,并且在Reduction Approach的条件下,讨论了局部鞍点与局部最优解之间的关系。首先由鞍点的存在性得到了问题的局部最优解。其次在扩展的MF约束条件、强二阶充分条件和扩展的强二阶充分条件下又得到了局部最优解是局部鞍点存在的充分条件。A class of semi-infinite programming problem has become a powerful tool for the mathematical modeling of many real-life problems in recent years.In this paper,augmented Lagrangian will be applied to the semi-infinite programming problem and their characterizations in terms of saddle points will be obtained.Under the Reduction Approach condition,the relation between the local saddle point and the local optimal solution will be discussed.Firstly,the local optimal solution of the problem is obtained by the existence of saddle points.Secondly,under EMFCQ SSOSC and ESSOSC conditions,the local optimal solution is the sufficient condition for the existence of the local saddle point.

关 键 词：半无限规划 增广拉格朗日 局部鞍点 

分 类 号：O221.2[理学—运筹学与控制论]