{"title":"Semicontinuity of the composition of set-valued map and scalarization function for sets","authors":"Mengxue Liu, Yuto Ogata, Tamaki Tanaka","doi":"10.23952/jano.1.2019.3.06","DOIUrl":null,"url":null,"abstract":"In this paper, we deal with the inheritation of the semicontinuity of set-valued maps via general scalarization for sets, which is regarded as the framework of generalizations of results by Kuwano, Tanaka, and Yamada in 2010. Since the unified scalarization functions for sets satisfy certain desired semicontinuity, our main theorems can be reduced to the results in earlier study.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"73 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Numerical Optimization","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23952/jano.1.2019.3.06","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, we deal with the inheritation of the semicontinuity of set-valued maps via general scalarization for sets, which is regarded as the framework of generalizations of results by Kuwano, Tanaka, and Yamada in 2010. Since the unified scalarization functions for sets satisfy certain desired semicontinuity, our main theorems can be reduced to the results in earlier study.
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