{"title":"非线性分析中的证明理论方法","authors":"U. Kohlenbach","doi":"10.1142/9789813272880_0045","DOIUrl":null,"url":null,"abstract":"We discuss applications of methods from proof theory, so-called proof interpretations, for the extraction of explicit bounds in convex optimization, fixed point theory, ergodic theory and nonlinear semigroup theory. Mathematics Subject Classification (2010): Primary 03F10; Secondary 03F35, 47H10, 47H20, 47H25, 90C30.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"49","resultStr":"{\"title\":\"PROOF-THEORETIC METHODS IN NONLINEAR ANALYSIS\",\"authors\":\"U. Kohlenbach\",\"doi\":\"10.1142/9789813272880_0045\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We discuss applications of methods from proof theory, so-called proof interpretations, for the extraction of explicit bounds in convex optimization, fixed point theory, ergodic theory and nonlinear semigroup theory. Mathematics Subject Classification (2010): Primary 03F10; Secondary 03F35, 47H10, 47H20, 47H25, 90C30.\",\"PeriodicalId\":318252,\"journal\":{\"name\":\"Proceedings of the International Congress of Mathematicians (ICM 2018)\",\"volume\":\"29 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"49\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the International Congress of Mathematicians (ICM 2018)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/9789813272880_0045\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the International Congress of Mathematicians (ICM 2018)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/9789813272880_0045","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We discuss applications of methods from proof theory, so-called proof interpretations, for the extraction of explicit bounds in convex optimization, fixed point theory, ergodic theory and nonlinear semigroup theory. Mathematics Subject Classification (2010): Primary 03F10; Secondary 03F35, 47H10, 47H20, 47H25, 90C30.
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