{"title":"论克拉克边际函数的次微分","authors":"G. Bouza, Ernest Quintana, C. Tammer","doi":"10.23952/asvao.3.2021.3.03","DOIUrl":null,"url":null,"abstract":"In this short note, we derive an upper estimate of Clarke’s subdifferential of marginal functions in Banach spaces. The structure of the upper estimate is very similar to other results already obtained in the literature. The novelty lies on the fact that we derive our assertions in general Banach spaces, and avoid the use of the Asplund assumption.","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"43 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Clarke’s subdifferential of marginal functions\",\"authors\":\"G. Bouza, Ernest Quintana, C. Tammer\",\"doi\":\"10.23952/asvao.3.2021.3.03\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this short note, we derive an upper estimate of Clarke’s subdifferential of marginal functions in Banach spaces. The structure of the upper estimate is very similar to other results already obtained in the literature. The novelty lies on the fact that we derive our assertions in general Banach spaces, and avoid the use of the Asplund assumption.\",\"PeriodicalId\":362333,\"journal\":{\"name\":\"Applied Set-Valued Analysis and Optimization\",\"volume\":\"43 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Set-Valued Analysis and Optimization\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.23952/asvao.3.2021.3.03\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Set-Valued Analysis and Optimization","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23952/asvao.3.2021.3.03","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this short note, we derive an upper estimate of Clarke’s subdifferential of marginal functions in Banach spaces. The structure of the upper estimate is very similar to other results already obtained in the literature. The novelty lies on the fact that we derive our assertions in general Banach spaces, and avoid the use of the Asplund assumption.
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