An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows (Second Edition)
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| Title: | An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows (Second Edition) |
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| Description: | This book provides a self-contained introduction to optimal transport, and it is intended as a starting point for any researcher who wants to enter into this beautiful subject. The presentation focuses on the essential topics of the theory: Kantorovich duality, existence and uniqueness of optimal transport maps, Wasserstein distances, the JKO scheme, Otto's calculus, and Wasserstein gradient flows. At the end, a presentation of some selected applications of optimal transport is given. Suitable for a course at the graduate level, the book also includes an appendix with a series of exercises along with their solutions. The present second edition contains a number of additions, such as a new section on the Brunn–Minkowski inequality, new exercises, and various corrections throughout the text. |
| Authors: | Alessio Figalli, Federico Glaudo |
| Resource Type: | eBook. |
| Subjects: | Flows (Differentiable dynamical systems), Transportation problems (Programming), Mathematical optimization |
| Categories: | MATHEMATICS / Mathematical Analysis, COMPUTERS / Programming / Algorithms |
| Database: | eBook Collection (EBSCOhost) |
| Abstract: | This book provides a self-contained introduction to optimal transport, and it is intended as a starting point for any researcher who wants to enter into this beautiful subject. The presentation focuses on the essential topics of the theory: Kantorovich duality, existence and uniqueness of optimal transport maps, Wasserstein distances, the JKO scheme, Otto's calculus, and Wasserstein gradient flows. At the end, a presentation of some selected applications of optimal transport is given. Suitable for a course at the graduate level, the book also includes an appendix with a series of exercises along with their solutions. The present second edition contains a number of additions, such as a new section on the Brunn–Minkowski inequality, new exercises, and various corrections throughout the text. |
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| ISBN: | 9783985470501 9783985475506 |
