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Convex duality in nonlinear optimal transport

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Convex duality in nonlinear optimal transport. / Pennanen, Teemu ; Perkkio, Ari-Pekka.

In: JOURNAL OF FUNCTIONAL ANALYSIS, Vol. 277, No. 4, 15.08.2019, p. 1029-1060.

Research output: Contribution to journalArticle

Harvard

Pennanen, T & Perkkio, A-P 2019, 'Convex duality in nonlinear optimal transport', JOURNAL OF FUNCTIONAL ANALYSIS, vol. 277, no. 4, pp. 1029-1060. https://doi.org/10.1016/j.jfa.2019.04.010

APA

Pennanen, T., & Perkkio, A-P. (2019). Convex duality in nonlinear optimal transport. JOURNAL OF FUNCTIONAL ANALYSIS, 277(4), 1029-1060. https://doi.org/10.1016/j.jfa.2019.04.010

Vancouver

Pennanen T, Perkkio A-P. Convex duality in nonlinear optimal transport. JOURNAL OF FUNCTIONAL ANALYSIS. 2019 Aug 15;277(4):1029-1060. https://doi.org/10.1016/j.jfa.2019.04.010

Author

Pennanen, Teemu ; Perkkio, Ari-Pekka. / Convex duality in nonlinear optimal transport. In: JOURNAL OF FUNCTIONAL ANALYSIS. 2019 ; Vol. 277, No. 4. pp. 1029-1060.

Bibtex Download

@article{be8bf6fc59844a18b9ec00419bd0a1ce,
title = "Convex duality in nonlinear optimal transport",
abstract = "This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows for generalizations of the classical problem formulations. General results on convex duality yield dual problems and optimality conditions for these problems. When the objective takes the form of a convex integral functional, we obtain more explicit optimality conditions and establish the existence of solutions for a relaxed formulation of the problem. This covers, in particular, the mass transportation problem and its nonlinear generalizations.",
keywords = "Convex duality, Integral functionals, Martingale transport, Schr{\"o}dinger problem",
author = "Teemu Pennanen and Ari-Pekka Perkkio",
year = "2019",
month = aug,
day = "15",
doi = "10.1016/j.jfa.2019.04.010",
language = "English",
volume = "277",
pages = "1029--1060",
journal = "JOURNAL OF FUNCTIONAL ANALYSIS",
issn = "0022-1236",
publisher = "ACADEMIC PRESS INC",
number = "4",

}

RIS (suitable for import to EndNote) Download

TY - JOUR

T1 - Convex duality in nonlinear optimal transport

AU - Pennanen, Teemu

AU - Perkkio, Ari-Pekka

PY - 2019/8/15

Y1 - 2019/8/15

N2 - This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows for generalizations of the classical problem formulations. General results on convex duality yield dual problems and optimality conditions for these problems. When the objective takes the form of a convex integral functional, we obtain more explicit optimality conditions and establish the existence of solutions for a relaxed formulation of the problem. This covers, in particular, the mass transportation problem and its nonlinear generalizations.

AB - This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows for generalizations of the classical problem formulations. General results on convex duality yield dual problems and optimality conditions for these problems. When the objective takes the form of a convex integral functional, we obtain more explicit optimality conditions and establish the existence of solutions for a relaxed formulation of the problem. This covers, in particular, the mass transportation problem and its nonlinear generalizations.

KW - Convex duality

KW - Integral functionals

KW - Martingale transport

KW - Schrödinger problem

UR - http://www.scopus.com/inward/record.url?scp=85066406473&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2019.04.010

DO - 10.1016/j.jfa.2019.04.010

M3 - Article

VL - 277

SP - 1029

EP - 1060

JO - JOURNAL OF FUNCTIONAL ANALYSIS

JF - JOURNAL OF FUNCTIONAL ANALYSIS

SN - 0022-1236

IS - 4

ER -

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