The $\infty$-Wasserstein distance: local solutions and existence of optimal transport maps

created by depascal on 07 May 2008

[BibTeX]

Published Paper

Inserted: 7 may 2008

Journal: SIAM Journal of Mathematical Analysis
Volume: 40
Number: 1
Pages: 1-20
Year: 2008

Abstract:

We consider the non-nonlinear optimal transportation problem of minimizing the cost functional $\C_\infty(\lambda)= \lambda\text{-}\esssup_{(x,y) \in \Omega^2} y-x$ in the set of probability measures on $\Omega^2$ having prescribed marginals. This corresponds to the question of characterizing the measures that realize the infinite Wasserstein distance. We establish the existence of local'' solutions and characterize this class with the aid of an adequate version of cyclical monotonicity. Moreover, under natural assumptions, we show that local solutions are induced by transport maps.

Download:

Credits | Cookie policy | HTML 5 | CSS 2.1