Optimal Transport for Applied Mathematicians

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

The role of optimal transport in applied mathematics is dramatically increasing, with applications in economics, finance, potential games, image processing and fluid dynamics

Each chapter includes a section in which specific applications of optimal transport are discussed in relation to the mathematics presented

Covers topics not found in other books on optimal transport, including the Knothe transport, the Dacorogna-Moser flow and the case of the supremal cost

Inhaltsverzeichnis

Preface.- Primal and Dual Problems.- One-Dimensional Issues.- L^1 and L^infinity Theory.- Minimal Flows.- Wasserstein Spaces.- Numerical Methods.- Functionals over Probabilities.- Gradient Flows.- Exercises.- References.- Index.

Erscheinungsjahr:	2015
Fachbereich:	Allgemeines
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Progress in Nonlinear Differential Equations and Their Applications
Inhalt:	xxvii 353 S.
ISBN-13:	9783319208275
ISBN-10:	3319208276
Sprache:	Englisch
Herstellernummer:	978-3-319-20827-5
Einband:	Gebunden
Autor:	Santambrogio, Filippo
Hersteller:	Springer-Verlag GmbH Springer International Publishing AG Birkhäuser
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Abbildungen:	11 schwarz-weiße und 20 farbige Abbildungen, Bibliographie
Maße:	241 x 160 x 25 mm
Von/Mit:	Filippo Santambrogio
Erscheinungsdatum:	27.10.2015
Gewicht:	0,81 kg