Optimal Transport pp 51-92

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 338)

Cyclical monotonicity and Kantorovich duality

Abstract

To go on, we should become acquainted with two basic concepts in the theory of optimal transport. The first one is a geometric property called cyclical monotonicity; the second one is the Kantorovich dual problem, which is another face of the original Monge—Kantorovich problem. The main result in this chapter is Theorem 5.10.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Unité de Mathématiques Pures t Appliquées (UMPA)École Normale Supérieure de LyonLyon CX 07France

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