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Optimal transport for applied mathem...

Santambrogio, Filippo.

Optimal transport for applied mathematicianscalculus of variations, PDEs, and modeling /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Optimal transport for applied mathematiciansby Filippo Santambrogio.
Reminder of title:	calculus of variations, PDEs, and modeling /
Author:	Santambrogio, Filippo.
Published:	Cham :Springer International Publishing :2015.
Description:	xxvii, 353 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Mathematical optimization.
Online resource:	http://dx.doi.org/10.1007/978-3-319-20828-2
ISBN:	9783319208282$q(electronic bk.)

Optimal transport for applied mathematicianscalculus of variations, PDEs, and modeling /
Santambrogio, Filippo.

Optimal transport for applied mathematicianscalculus of variations, PDEs, and modeling /[electronic resource] :by Filippo Santambrogio. - Cham :Springer International Publishing :2015. - xxvii, 353 p. :ill., digital ;24 cm. - Progress in nonlinear differential equations and their applications,v.871421-1750 ;. - Progress in nonlinear differential equations and their applications ;v.83..

This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource.

ISBN: 9783319208282$q(electronic bk.)

Standard No.: 10.1007/978-3-319-20828-2doiSubjects--Topical Terms:

183292
Mathematical optimization.

LC Class. No.: QA402.5

Dewey Class. No.: 519.6

Optimal transport for applied mathematicianscalculus of variations, PDEs, and modeling /
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520 $a This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource.
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