Constrained Optimal Transport

Ibrahim Ekren; H. Mete Soner

doi:10.1007/s00205-017-1178-0

Constrained Optimal Transport

Ibrahim Ekren, H. Mete Soner

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

The classical duality theory of Kantorovich (C R (Doklady) Acad Sci URSS (NS) 37:199–201, 1942) and Kellerer (Z Wahrsch Verw Gebiete 67(4):399–432, 1984) for classical optimal transport is generalized to an abstract framework and a characterization of the dual elements is provided. This abstract generalization is set in a Banach lattice X with an order unit. The problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of X and the dual problem is defined on the bi-dual of X. These results are then applied to several extensions of the classical optimal transport.

Original language	English (US)
Pages (from-to)	929-965
Number of pages	37
Journal	Archive for Rational Mechanics and Analysis
Volume	227
Issue number	3
DOIs	https://doi.org/10.1007/s00205-017-1178-0
State	Published - Mar 1 2018
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

Access to Document

10.1007/s00205-017-1178-0

Cite this

@article{c6228a61fb6040faac976cef846d3008,

title = "Constrained Optimal Transport",

abstract = "The classical duality theory of Kantorovich (C R (Doklady) Acad Sci URSS (NS) 37:199–201, 1942) and Kellerer (Z Wahrsch Verw Gebiete 67(4):399–432, 1984) for classical optimal transport is generalized to an abstract framework and a characterization of the dual elements is provided. This abstract generalization is set in a Banach lattice X with an order unit. The problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of X and the dual problem is defined on the bi-dual of X. These results are then applied to several extensions of the classical optimal transport.",

author = "Ibrahim Ekren and Soner, {H. Mete}",

note = "Publisher Copyright: {\textcopyright} 2017, Springer-Verlag GmbH Germany.",

year = "2018",

month = mar,

day = "1",

doi = "10.1007/s00205-017-1178-0",

language = "English (US)",

volume = "227",

pages = "929--965",

journal = "Archive for Rational Mechanics and Analysis",

issn = "0003-9527",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Constrained Optimal Transport

AU - Ekren, Ibrahim

AU - Soner, H. Mete

PY - 2018/3/1

Y1 - 2018/3/1

N2 - The classical duality theory of Kantorovich (C R (Doklady) Acad Sci URSS (NS) 37:199–201, 1942) and Kellerer (Z Wahrsch Verw Gebiete 67(4):399–432, 1984) for classical optimal transport is generalized to an abstract framework and a characterization of the dual elements is provided. This abstract generalization is set in a Banach lattice X with an order unit. The problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of X and the dual problem is defined on the bi-dual of X. These results are then applied to several extensions of the classical optimal transport.

AB - The classical duality theory of Kantorovich (C R (Doklady) Acad Sci URSS (NS) 37:199–201, 1942) and Kellerer (Z Wahrsch Verw Gebiete 67(4):399–432, 1984) for classical optimal transport is generalized to an abstract framework and a characterization of the dual elements is provided. This abstract generalization is set in a Banach lattice X with an order unit. The problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of X and the dual problem is defined on the bi-dual of X. These results are then applied to several extensions of the classical optimal transport.

UR - http://www.scopus.com/inward/record.url?scp=85030871115&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030871115&partnerID=8YFLogxK

U2 - 10.1007/s00205-017-1178-0

DO - 10.1007/s00205-017-1178-0

M3 - Article

AN - SCOPUS:85030871115

SN - 0003-9527

VL - 227

SP - 929

EP - 965

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 3

ER -

Constrained Optimal Transport

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this