一类多边际最优运输问题中周期单调性的充分性

IF 2.3 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics Pub Date : 2024-05-14 DOI:10.1017/s0956792524000202

Luigi De Pascale, Anna Kausamo

{"title":"一类多边际最优运输问题中周期单调性的充分性","authors":"Luigi De Pascale, Anna Kausamo","doi":"10.1017/s0956792524000202","DOIUrl":null,"url":null,"abstract":"<img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240513153132896-0623:S0956792524000202:S0956792524000202_inline2.png\">$c$</img>-cyclical monotonicity is the most important optimality condition for an optimal transport plan. While the proof of necessity is relatively easy, the proof of sufficiency is often more difficult or even elusive. We present here a new approach, and we show how known results are derived in this new framework and how this approach allows to prove sufficiency in situations previously not treatable.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"66 1","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sufficiency of -cyclical monotonicity in a class of multi-marginal optimal transport problems\",\"authors\":\"Luigi De Pascale, Anna Kausamo\",\"doi\":\"10.1017/s0956792524000202\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240513153132896-0623:S0956792524000202:S0956792524000202_inline2.png\\\">$c$</img>-cyclical monotonicity is the most important optimality condition for an optimal transport plan. While the proof of necessity is relatively easy, the proof of sufficiency is often more difficult or even elusive. We present here a new approach, and we show how known results are derived in this new framework and how this approach allows to prove sufficiency in situations previously not treatable.\",\"PeriodicalId\":51046,\"journal\":{\"name\":\"European Journal of Applied Mathematics\",\"volume\":\"66 1\",\"pages\":\"\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2024-05-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s0956792524000202\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0956792524000202","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

c$周期单调性是最优运输计划最重要的最优性条件。必要性的证明相对容易，但充分性的证明往往比较困难，甚至难以捉摸。我们在此介绍一种新方法，并展示如何在这一新框架下推导出已知结果，以及这种方法如何在以前无法处理的情况下证明充分性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Sufficiency of -cyclical monotonicity in a class of multi-marginal optimal transport problems

$c$-cyclical monotonicity is the most important optimality condition for an optimal transport plan. While the proof of necessity is relatively easy, the proof of sufficiency is often more difficult or even elusive. We present here a new approach, and we show how known results are derived in this new framework and how this approach allows to prove sufficiency in situations previously not treatable.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

European Journal of Applied Mathematics 数学-应用数学

CiteScore

4.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Since 2008 EJAM surveys have been expanded to cover Applied and Industrial Mathematics. Coverage of the journal has been strengthened in probabilistic applications, while still focusing on those areas of applied mathematics inspired by real-world applications, and at the same time fostering the development of theoretical methods with a broad range of applicability. Survey papers contain reviews of emerging areas of mathematics, either in core areas or with relevance to users in industry and other disciplines. Research papers may be in any area of applied mathematics, with special emphasis on new mathematical ideas, relevant to modelling and analysis in modern science and technology, and the development of interesting mathematical methods of wide applicability.