Chapter

Optimal Transport

Volume 338 of the series Grundlehren der mathematischen Wissenschaften pp 51-92

Cyclical monotonicity and Kantorovich duality

  • Cédric VillaniAffiliated withUnité de Mathématiques Pures t Appliquées (UMPA), École Normale Supérieure de Lyon Email author 

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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.