文献类型：期刊文献

英文题名：Mordukhovich stationarity for mathematical programs with switching constraints under weak constraint qualifications

作者：Li, Gaoxi[1,2,3];Guo, Lei[4]

机构：[1]Chongqing Technol & Business Univ, Sch Math & Stat, Chongqing, Peoples R China;[2]Univ Elect Sci & Technol China, Sch Math Sci, Chengdu, Peoples R China;[3]Chongqing Key Lab Social Econ & Appl Stat, Chongqing, Peoples R China;[4]East China Univ Sci & Technol, Sch Business, Shanghai, Peoples R China

年份：2023

卷号：72

期号：7

起止页码：1817

外文期刊名：OPTIMIZATION

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000800873100001)】；

基金：This first author was supported in part by NSFC Grants (No. 11901068,11871383), the Project of Chongqing Technology and Business University (No. 1952034,ZDPTTD201908) and the Project of National Center for Applied Mathematics (No. ncamc2021-msxm01). This second author was supported in part by the Natural Science Foundation of Shanghai (No. 22ZR1415900), the National Natural Science Foundation of China (No. 72131007) and the Fundamental Research Funds for the Central Universities.

语种：英文

外文关键词：Mathematical program with switching constraints; constraint qualification; stationarity

摘要：The mathematical program with switching constraints (MPSC), which has been introduced recently, is a difficult class of optimization problems since standard constraint qualifications are very likely to fail at local minimizers. Due to the failure of standard constraint qualifications, it is reasonable to propose some constraint qualifications for local minimizers to satisfy some stationarity conditions that are generally weaker than Karush-Kuhn-Tucker stationarity such as Mordukhovich (M-) stationarity. First, we propose the weakest constraint qualification for M-stationarity of MPSC to hold at local minimizers. Then we extend some weak verifiable constraint qualifications for nonlinear programming to allow the existence of switching constraints, which are all strictly weaker than MPSC linear independence constraint qualification and/or MPSC Mangasarian-Fromovitz constraint qualification used in the literature. We show that most of the newly introduced constraint qualifications are sufficient for local minimizers to be M-stationary. Finally, the relations among MPSC tailored constraint qualifications are discussed.