Optimal transport for applied mathematicians : calculus of variations, PDEs, and modeling /
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 r...
| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Cham :
Birkhäuser,
c2015
[Cham] : Birkhäuser, ©2015 Cham : [2015] Cham, Switzerland : 2022 |
| Series: | Progress in nonlinear differential equations and their applications ;
v. 87 Progress in nonlinear differential equations and their applications |
| Subjects: |
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| 100 | 1 | |a Santambrogio, Filippo | |
| 100 | 1 | |a Santambrogio, Filippo, |e author | |
| 245 | 1 | 0 | |a Optimal transport for applied mathematicians : |b calculus of variations, PDEs, and modeling / |c Filippo Santambrogio |
| 260 | |a Cham : |b Birkhäuser, |c c2015 | ||
| 260 | |a [Cham] : |b Birkhäuser, |c ©2015 | ||
| 264 | 1 | |a Cham : |b Birkhäuser, |c [2015] | |
| 264 | 1 | |a Cham, Switzerland : |b Birkhäuser, |c 2022 | |
| 264 | 4 | |c ©2015 | |
| 300 | |a xxvii, 353 p. : |b ill. (some col.) ; |c 25 cm | ||
| 300 | |a xxvii, 353 pages : |b illustrations ; |c 25 cm | ||
| 300 | |a xxvii-353 pages : |b illustrations ; |c 24 cm | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a unmediated |b n |2 rdamedia | ||
| 338 | |a volume |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in nonlinear differential equations and their applications | |
| 490 | 1 | |a Progress in nonlinear differential equations and their applications, |x 1421-1750 ; |v v. 87 | |
| 504 | |a Includes bibliographic references and index | ||
| 504 | |a Includes bibliographical references (p. 339-350) and index | ||
| 504 | |a Includes bibliographical references (pages 339-350) and index | ||
| 505 | 0 | |a 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 | |
| 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 | ||
| 530 | |a Also available in an electronic version | ||
| 650 | 0 | |a Calculus of variations | |
| 650 | 0 | |a Control theory | |
| 650 | 0 | |a Differential equations, Partial | |
| 650 | 0 | |a Mathematical optimization | |
| 650 | 0 | |a Transport theory | |
| 650 | 7 | |a Calculus of variations |2 fast | |
| 650 | 7 | |a Control theory |2 fast | |
| 650 | 7 | |a Mathematical optimization |2 fast | |
| 650 | 7 | |a Transport theory |2 fast | |
| 830 | 0 | |a Progress in nonlinear differential equations and their applications ; |v v. 87 | |
| 830 | 0 | |a Progress in nonlinear differential equations and their applications | |
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