半无限规划的增广拉格朗日对偶理论  

Duality of Semi-infinite Programming via Augmented Lagrangian

作　　者：苏珂[1,2] 王晨 林雨萌[1,2] SU Ke;WANG Chen;LIN Yumeng(College of Mathematics and Information Science,Hebei University,Baoding 071002,China;Hebei Province Key Laboratory of Machine Learning and Computational Intelligence,Baoding 071002,China)

机构地区：[1]河北大学数学与信息科学学院,河北保定071002 [2]河北省机器学习与计算智能重点实验室,河北保定071002

出　　处：《应用数学》2021年第4期894-900,共7页Mathematica Applicata

基　　金：Supported by Post-graduate’s Innovation Fund Project of Hebei University(hbu2020ss043);Hebei Provience Nature Science Foundation of China (A2018201172)。

摘　　要：本文主要研究带有不等式约束的非凸半无限规划的对偶问题.众所周知,运用标准的拉格朗日函数构造对偶问题通常会存在对偶间隙,为了消除对偶间隙,我们构造一个增广拉格朗日函数,然后讨论对偶性.在合理的假设下,原问题与增广拉格朗日对偶问题之间的强对偶性成立.最后,通过一个算例对结果进行了验证.In this paper, we mainly study the dual problem of the nonconvex semi-infinite programming problem with inequality constraints. It is well known that there is usually a duality gap in constructing duality problem using the ordinary Lagrangian function. To eliminate the duality gap, we construct an augmented Lagrangian function, then discuss its duality. Under reasonable assumptions, the strong duality theorem between the primal problem and the augmented Lagrangian dual problem holds. Finally, an example is given to verify the presented results.

关 键 词：半无限规划 非凸性 对偶性 增广拉格朗日函数 

分 类 号：O221.2[理学—运筹学与控制论]