An invitation to optimal transport, Wasserstein distances, and gradient flows / Alessio Figalli, Federico Glaudo.

Format:

Book

Author/Creator:

Figalli, Alessio, 1984- author.

Glaudo, Federico, author.

Series:

EMS textbooks in mathematics

Language:

English

Subjects (All):

Transportation problems (Programming).

Flows (Differentiable dynamical systems).

Mathematical optimization.

Physical Description:

vi, 146 pages ; 25 cm.

Edition:

Second edition.

Place of Publication:

Berlin, Germany : EMS Press, [2023]

Summary:

"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. The book is suitable for a course at the graduate level and 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."-- publisher

Contents:

Introduction

Optimal transport

Wasserstein distances and gradient flow

Differential viewpoint of optimal transport

Further reading.

Notes:

Includes bibliographical references.

ISBN:

9783985470501

3985470502

OCLC:

1391145176

Publisher Number:

99996553316