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Optimal Transportation: Theory and applications

Yann Ollivier 1, 2 Hervé Pajot 3 Cédric Villani 4
2 TAO - Machine Learning and Optimisation
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LRI - Laboratoire de Recherche en Informatique
4 EDPA - Équations aux dérivées partielles, analyse
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : The theory of optimal transportation has its origins in the eighteenth century when the problem of transporting resources at a minimal cost was first formalised. Through subsequent developments, particularly in recent decades, it has become a powerful modern theory. This book contains the proceedings of the summer school 'Optimal Transportation: Theory and Applications' held at the Fourier Institute in Grenoble. The event brought together mathematicians from pure and applied mathematics, astrophysics, economics and computer science. Part I of this book is devoted to introductory lecture notes accessible to graduate students, while Part II contains research papers. Together, they represent a valuable resource on both fundamental and advanced aspects of optimal transportation, its applications, and its interactions with analysis, geometry, PDE and probability, urban planning and economics. Topics covered include Ricci flow, the Euler equations, functional inequalities, curvature-dimension conditions, and traffic congestion.
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Submitted on : Monday, January 19, 2015 - 11:08:19 AM
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  • HAL Id : hal-01104763, version 1


Yann Ollivier, Hervé Pajot, Cédric Villani. Optimal Transportation: Theory and applications. Yann Ollivie; Hervé Pajo; Cédric Villani. Summer school on Optimal transportation, 2009, Grenoble, France. 413, Cambridge University Press, 2014, London Mathematical Society Lecture Note Series, 9781107689497. ⟨hal-01104763⟩



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