半无限规划中的增广拉格朗日鞍点

Saddle Points of Augmented Lagrangian for Semi-infinite Programming

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.