MPVCC问题的M稳定性的序列最优性条件研究  

The sequential optimality condition for M-stationarity for MPVCC

作　　者：许娜 姜姗 沈洁[1] XU Na;JIANG Shan;SHEN Jie(School of Mathematics, Liaoning Normal University, Dalian 116029, China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2022年第1期13-19,共7页Journal of Liaoning Normal University:Natural Science Edition

基　　金：辽宁省教育厅科学研究青年项目(LQ2019019)。

摘　　要：带有垂直互补约束的数学规划(MPVCC)问题是一类重要的优化问题,这类问题在很多领域都有着广泛的应用.在过去的几年中,人们非常关注非线性规划的序列最优性条件,因为它与算法的停止准则密切相关,在收敛性分析中也发挥着重要的作用.给出了MPVCC问题关于M稳定性的序列最优性条件,即AM稳定性.此外,还给出了与之相关的保证M稳定性的约束规范.最后,讨论了新旧约束规范之间的关系.Mathematical program with vertical complementarity constraints(MPVCC)is an important class of optimization problems as it arises frequently in a broad spectrum of fields.In the last few years,special attention has been devoted to the sequential optimality condition for nonlinear constrained optimization.It is closely related to the stopping criteria of algorithms and is a useful tool for the improvement of convergence analysis.In this paper,we present a sequential optimality condition for M-stationarity for MPVCC,namely,AM-stationarity.Furthermore,the constraint qualification for M-stationarity associated with such sequential optimality condition is presented.Finally,we discuss the relations between the old and new constraint qualifications.

关 键 词：带有垂直互补约束的数学规划问题 序列最优性条件 约束规范 

分 类 号：O224[理学—运筹学与控制论]