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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2022. Vol 41

Nonlinear Kantorovich Problems with a Parameter

Author(s)
Vladimir I. Bogachev1,2,3,4, Ilya I. Malofeev2,3

1Lomonosov Moscow State University, Moscow, Russian Federation

2National Research University Higher School of Economics, Moscow, Russian Federation

3Saint Tikhon’s Orthodox University, Moscow, Russian Federation

4Moscow Center for Fundamental and Applied Mathematics, Moscow, Russian Federation

Abstract
We consider nonlinear Kantorovich problems with marginal distributions and cost functions depending measurably on a parameter and prove that there exist optimal transportation plans that are also measurable with respect to the parameter. Unlike the classical linear Kantorovich problem of minimization of the integrals of a given cost function with respect to transportation plans, we deal with nonlinear cost functionals in which integrands depend on transportation plans. Dependence of cost functions on conditional measures of transportation plans is also allowed.
About the Authors

Vladimir I. Bogachev, Dr. Sci. (Phys.–Math.), Prof., Moscow State University, Moscow, 119991, Russian Federation, vibogach@mail.ru

Ilya I. Malofeev, Cand. Sci. (Phys.Math.), Researcher, National Research University Higher School of Economics, Moscow, 101000, Russian Federation, ilmalofeev@yandex.ru

For citation
Bogachev V. I., Malofeev I. I. Nonlinear Kantorovich Problems with a Parameter. The Bulletin of Irkutsk State University. Series Mathematics, 2022, vol. 41, pp. 96–106. https://doi.org/10.26516/1997-7670.2022.41.96
Keywords
Kantorovich problem, optimal plan, measurability with respect to a parameter
UDC
517.9
MSC
49Q22, 28C15, 28A33, 46E27
DOI
https://doi.org/10.26516/1997-7670.2022.41.96
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