一个求解消失约束数学规划的部分光滑正则化方法  

A Partly Smoothing-Regularization Method for Mathematical Programs with Vanishing Constraints

作　　者：董艳凤 初德建 胡林玉 胡清洁 DONG Yanfeng;CHU Dejian;HU Linyu;HU Qingjie(Guangxi Key Laboratory of Automatic Detecting Technology and Instruments,Guilin 541004,China;Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation,Guilin 541004,China;School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]广西自动检测技术与仪器重点实验室,广西桂林541004 [2]广西高校数据分析与计算重点实验室,广西桂林541004 [3]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《应用数学》2021年第1期163-175,共13页Mathematica Applicata

基　　金：Supported by NNSF of China (11461015,11761014,11961011);the Guangxi Natural Science Foundation (2015GXNSFAA139010,2017GXNSFAA198243);the National Innovation Project of University Students(201910595040);the Guangxi Key Labovatory of Automatic Detecting Technology (YQ17117)。

摘　　要：本文研究带有消失约束的数学规划问题.针对这一问题,我们提出了一种基于伪Huber函数的光滑正则化方法,该方法只对部分消失约束进行光滑化.对于新的光滑问题,我们证明Mangasarian-Fromovitz约束规格在某些情况下是成立的.我们也分析该方法的收敛性质,即,一个光滑正则化问题稳定点序列的聚点是原问题的T-稳定点,并给出光滑正则化问题稳定点序列的聚点是原问题的M-稳定点或S-稳定点的一些充分条件.最后初步的数值结果表明该方法是可行的.In this paper,we consider the mathematical programs with vanishing constraints(MPVC).We present a pseudo Huber function based smoothing-regularization method for this problem,which only makes the part ones of the vanishing constraints be smoothed.For the new smoothed problem,we show that the Mangasarian-Fromovitz constraints qualification(MFCQ) holds under some conditions.We also analyze the convergence behavior of the smoothing-regularization method,i.e.,an accumulation point of the stationary points sequence for the smoothing-regularization problem is a T-stationary point,and obtain some sufficient conditions such that an accumulation point of the stationary points sequence for the smoothing-regularization problem is M-or S-stationarity,respectively.Finally,some preliminary numerical results show that the proposed method may be promising.

关 键 词：消失约束数学规划 T-稳定点 M-稳定点 S-稳定点 数值结果 

分 类 号：O221[理学—运筹学与控制论]