A Class of Smoothing-regularization Methods to Mathematical Programs with Vanishing Constraints  

消失约束数学规划问题的一类光滑正则化方法

作　　者：HU Qingjie MA Lili CHEN Yu 胡清洁;马丽丽;陈玉(桂林电子科技大学数学与计算科学学院,广西高校数据分析与计算重点实验室,广西桂林541002;广西应用数学中心(GUET),广西桂林541004;广东科技学院通识教育中心,广东东莞523668;广西师范大学数学与统计学院,广西桂林541004)

机构地区：[1]School of Mathematics and Computing Science,Guangci Colleges and Universities Key Laboratory of Data Analysis and Computation,Guilin University of Electronic Technology,Guilin,Guangci,541002,P.R.China [2]Center for Applied Mathematics of Guangri(GUET),Guilin,Guangri,541002,P.R.China [3]College of General Education,Guangdong University of Science and Technology,Dongguan,Guangdong,523668,P.R.China [4]School of Mathematics and Statistics,Guangri Normal University,Guilin,Guangci,541004,P.R.China

出　　处：《数学进展》2024年第5期953-973,共21页Advances in Mathematics（China）

基　　金：Supported in part by NSFC(No.11961011);Guangxi Science and Technology Base and Talents Special Project(No.2021AC06001).

摘　　要：this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing constraints.These methods include the smoothing-regularization method proposed by Kanzow et al.in[Comput.Optim.Appl.,2013,55(3):733-767]as a special case.Under the weaker conditions than the ones that have been used by Kanzow et al.in 2013,we prove that the Mangasarian-Fromovitz constraint qualification holds at the feasible points of smoothing-regularization problem.We also analyze that the convergence behavior of the proposed smoothing-regularization method under mild conditions,i.e.,any accumulation point of the stationary point sequence for the smoothing-regularization problem is a strong stationary point.Finally,numerical experiments are given to show the efficiency of the proposed methods.本文提出了一类求解消失约束数学规划问题的光滑正则化方法,这些方法包括Kan-zow等人在[Comput。Optim.Appl.,2013,55(3):733-767]中提出的光滑正则化方法.在比Kanzow等2013年给出条件弱的情况下,证明了在光滑正则化问题的可行点处Mangasarian-Fromovitz约束规格成立,也分析了所提出的光滑正则化方法在一定条件下的收敛性,即光滑正则化问题稳定点序列的任意聚点为消失约束数学规划的一个强稳定点.最后通过数值实验验证了该方法的有效性。

关 键 词：mathematical programs with vanishing constraints smoothing-regularization method VC-MFCQ strong stationary point 

分 类 号：O221.2[理学—运筹学与控制论]