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arXiv · 2008.07926

The multistochastic Monge-Kantorovich problem

Nikita A. Gladkov·Alexander V. Kolesnikov·Alexander P. Zimin
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Abstract

The multistsochastic Monge--Kantorovich problem on the product $X = \prod_{i=1}^n X_i$ of $n$ spaces is a generalization of the multimarginal Monge--Kantorovich problem. For a given integer number $1 \le k<n$ we consider the minimization problem $\int c d \pi \to \inf$ of the space of measures with fixed projections onto every $X_{i_1} \times \dots \times X_{i_k}$ for arbitrary set of $k$ indices $\{i_1, \dots, i_k\} \subset \{1, \dots, n\}$. In this paper we study basic properties of the multistochastic problem, including well-posedness, existence of a dual solution, boundedness and continuity of a dual solution.

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Nikita A. Gladkov, Alexander V. Kolesnikov, Alexander P. Zimin. 2020-08-18. The multistochastic Monge-Kantorovich problem. https://arxiv.org/abs/2008.07926

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