The ... optimal transport: infinite cyclical monotonicity and the existence of optimal transport maps

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).We study the nonlinear optimal transportation problem of minimizing the functional ... among transport plans with given marginals. We present some general results regarding the problem, particularly connecting "good&quo...

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Bibliographic Details
Published inCalculus of variations and partial differential equations Vol. 52; no. 1-2; pp. 303 - 326
Main Author Jylhae, Heikki
Format Journal Article
LanguageEnglish
Published 01.01.2015
Subjects
Continuity
Joining
Mathematical analysis
Optimization
Texts
Transport
Transportation problem
Uniqueness
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Summary:(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).We study the nonlinear optimal transportation problem of minimizing the functional ... among transport plans with given marginals. We present some general results regarding the problem, particularly connecting "good" solutions to a suitable definition of cyclical monotonicity. We show that cyclically monotone transport plans are induced by transport maps in ... under relatively general assumptions on the first marginal and the cost function. With additional assumptions we are also able to prove results about continuity and uniqueness of these optimal maps.
Bibliography:ObjectType-Article-1
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content type line 23
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-014-0713-1