论文标题
多层化的Monge-Kantorovich问题
The multistochastic Monge-Kantorovich problem
论文作者
论文摘要
$ n $ spaces的$ x = \ prod_ {i = 1}^n x_i $ of $ n $ spaces上的多运动僧侣 - 肯塔托维奇的问题是对多边形蒙加 - kantorovich问题的概括。 For a given integer number $1 \le k<n$ we consider the minimization problem $\int c d π\to \inf$ 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 \} $。在本文中，我们研究了多构化问题的基本特性，包括适当性，双重解决方案的存在，界限和双重解决方案的连续性。
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 $\int c d π\to \inf$ 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.
