{"title":"具有互补约束的数学规划在MPCC-GCQ下m -平稳性的一个新的初等证明","authors":"Felix Harder","doi":"10.46298/jnsao-2021-6903","DOIUrl":null,"url":null,"abstract":"It is known in the literature that local minimizers of mathematical programs\nwith complementarity constraints (MPCCs) are so-called M-stationary points, if\na weak MPCC-tailored Guignard constraint qualification (called MPCC-GCQ) holds.\nIn this paper we present a new elementary proof for this result. Our proof is\nsignificantly simpler than existing proofs and does not rely on deeper\ntechnical theory such as calculus rules for limiting normal cones. A crucial\ningredient is a proof of a (to the best of our knowledge previously open)\nconjecture, which was formulated in a Diploma thesis by Schinabeck.","PeriodicalId":250939,"journal":{"name":"Journal of Nonsmooth Analysis and Optimization","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"A new elementary proof for M-stationarity under MPCC-GCQ for\\n mathematical programs with complementarity constraints\",\"authors\":\"Felix Harder\",\"doi\":\"10.46298/jnsao-2021-6903\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is known in the literature that local minimizers of mathematical programs\\nwith complementarity constraints (MPCCs) are so-called M-stationary points, if\\na weak MPCC-tailored Guignard constraint qualification (called MPCC-GCQ) holds.\\nIn this paper we present a new elementary proof for this result. Our proof is\\nsignificantly simpler than existing proofs and does not rely on deeper\\ntechnical theory such as calculus rules for limiting normal cones. A crucial\\ningredient is a proof of a (to the best of our knowledge previously open)\\nconjecture, which was formulated in a Diploma thesis by Schinabeck.\",\"PeriodicalId\":250939,\"journal\":{\"name\":\"Journal of Nonsmooth Analysis and Optimization\",\"volume\":\"7 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-11-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Nonsmooth Analysis and Optimization\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/jnsao-2021-6903\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonsmooth Analysis and Optimization","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/jnsao-2021-6903","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A new elementary proof for M-stationarity under MPCC-GCQ for
mathematical programs with complementarity constraints
It is known in the literature that local minimizers of mathematical programs
with complementarity constraints (MPCCs) are so-called M-stationary points, if
a weak MPCC-tailored Guignard constraint qualification (called MPCC-GCQ) holds.
In this paper we present a new elementary proof for this result. Our proof is
significantly simpler than existing proofs and does not rely on deeper
technical theory such as calculus rules for limiting normal cones. A crucial
ingredient is a proof of a (to the best of our knowledge previously open)
conjecture, which was formulated in a Diploma thesis by Schinabeck.
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