From Knothe’s transport to Brenier’s map and a continuation method for optimal transport

Guillaume Carlier, Alfred Galichon () and Filippo Santambrogio
Additional contact information
Guillaume Carlier: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Filippo Santambrogio: LMO - Laboratoire de Mathématiques d'Orsay - UP11 - Université Paris-Sud - Paris 11 - CNRS - Centre National de la Recherche Scientifique

Post-Print from HAL

Abstract: A simple procedure to map two probability measures in ℝd is the so-called \emph{Knothe-Rosenblatt rearrangement}, which consists in rearranging monotonically the marginal distributions of the last coordinate, and then the conditional distributions, iteratively. We show that this mapping is the limit of solutions to a class of Monge-Kantorovich mass transportation problems with quadratic costs, with the weights of the coordinates asymptotically dominating one another. This enables us to design a continuation method for numerically solving the optimal transport problem.

Keywords: Optimal Transport; Rearrangement of Vector-Valued Maps; Knothe-Rosenblatt Transport; Continuation Methods (search for similar items in EconPapers)
Date: 2008-10
Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03473711v1
References: View complete reference list from CitEc
Citations:

Published in SIAM Journal on Mathematical Analysis, 2008, 41 (6), pp.2554 - 2576

Downloads: (external link)
https://sciencespo.hal.science/hal-03473711v1/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03473711

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().