Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows / Alessio Figalli.

Format:

Book

Author/Creator:

Figalli, Alessio, author.

Language:

English

Subjects (All):

Mathematical optimization.

Mathematical optimization--Computer simulation.

Physical Description:

1 online resource

Place of Publication:

Berlin : European Mathematical Society - EMS - Publishing House GmbH, 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:

Description based on publisher supplied metadata and other sources.

ISBN:

9783985475506