Arthur Stephanovitch, Anqi Dong, Tryphon T. Georgiou
{"title":"Optimal transport through a toll station","authors":"Arthur Stephanovitch, Anqi Dong, Tryphon T. Georgiou","doi":"10.1017/s0956792524000317","DOIUrl":null,"url":null,"abstract":"We address the problem of optimal transport with a quadratic cost functional and a constraint on the flux through a constriction along the path. The constriction, conceptually represented by a toll station, limits the flow rate across. We provide a precise formulation which, in addition, is amenable to generalization in higher dimensions. We work out in detail the case of transport in one dimension by proving existence and uniqueness of solution. Under suitable regularity assumptions, we give an explicit construction of the transport plan. Generalization of flux constraints to higher dimensions and possible extensions of the theory are discussed.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"214 1","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2024-09-18","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/s0956792524000317","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
We address the problem of optimal transport with a quadratic cost functional and a constraint on the flux through a constriction along the path. The constriction, conceptually represented by a toll station, limits the flow rate across. We provide a precise formulation which, in addition, is amenable to generalization in higher dimensions. We work out in detail the case of transport in one dimension by proving existence and uniqueness of solution. Under suitable regularity assumptions, we give an explicit construction of the transport plan. Generalization of flux constraints to higher dimensions and possible extensions of the theory are discussed.
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.
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