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 Mat. Zametki, 2015, Volume 98, Issue 5, Pages 664–683 (Mi mz10896)

On the Monge–Kantorovich Problem with Additional Linear Constraints

D. Zaev

National Research University "Higher School of Economics" (HSE), Moscow

Abstract: The Monge–Kantorovich problem with the following additional constraint is considered: the admissible transportation plan must become zero on a fixed subspace of functions. Different subspaces give rise to different additional conditions on transportation plans. The main results are stated in general form and can be carried over to a number of important special cases. They are also valid for the Monge–Kantorovich problem whose solution is sought for the class of invariant or martingale measures. We formulate and prove a criterion for the existence of an optimal solution, a duality assertion of Kantorovich type, and a necessary geometric condition on the support of the optimal measure similar to the standard condition for $c$-monotonicity.

Keywords: Monge–Kantorovich problem, optimal transportation plan, Kantorovich duality.

DOI: https://doi.org/10.4213/mzm10896

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English version:
Mathematical Notes, 2015, 98:5, 725–741

Bibliographic databases:

UDC: 519.2+517.98

Citation: D. Zaev, “On the Monge–Kantorovich Problem with Additional Linear Constraints”, Mat. Zametki, 98:5 (2015), 664–683; Math. Notes, 98:5 (2015), 725–741

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz10896
• https://doi.org/10.4213/mzm10896
• http://mi.mathnet.ru/eng/mz/v98/i5/p664

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Citing articles on Google Scholar: Russian citations, English citations
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