{"title":"通过最优传输度量的不动点迭代的通用界","authors":"Mario Bravo, T. Champion, R. Cominetti","doi":"10.23952/asvao.4.2022.3.04","DOIUrl":null,"url":null,"abstract":". We present a self-contained analysis of a particular family of metrics over the set of non-negative integers. We show that these metrics, which are defined through a nested sequence of optimal transport problems, provide tight estimates for general Krasnosel’skii-Mann fixed point iterations for non-expansive maps. We also describe some of their very special properties, including their monotonicity and the so-called convex quadrangle inequality that yields a greedy algorithm for computing them efficiently.","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Universal bounds for fixed point iterations via optimal transport metrics\",\"authors\":\"Mario Bravo, T. Champion, R. Cominetti\",\"doi\":\"10.23952/asvao.4.2022.3.04\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We present a self-contained analysis of a particular family of metrics over the set of non-negative integers. We show that these metrics, which are defined through a nested sequence of optimal transport problems, provide tight estimates for general Krasnosel’skii-Mann fixed point iterations for non-expansive maps. We also describe some of their very special properties, including their monotonicity and the so-called convex quadrangle inequality that yields a greedy algorithm for computing them efficiently.\",\"PeriodicalId\":362333,\"journal\":{\"name\":\"Applied Set-Valued Analysis and Optimization\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Set-Valued Analysis and Optimization\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.23952/asvao.4.2022.3.04\",\"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.4.2022.3.04","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Universal bounds for fixed point iterations via optimal transport metrics
. We present a self-contained analysis of a particular family of metrics over the set of non-negative integers. We show that these metrics, which are defined through a nested sequence of optimal transport problems, provide tight estimates for general Krasnosel’skii-Mann fixed point iterations for non-expansive maps. We also describe some of their very special properties, including their monotonicity and the so-called convex quadrangle inequality that yields a greedy algorithm for computing them efficiently.
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