In this paper we study theoretical properties of the entropy-transport functional with repulsive cost functions. We provide sufficient conditions for the existence of a minimizer in a class of metric spaces and prove the \(\Gamma \)-convergence of the entropy-transport functional to a multi-marginal optimal transport problem with a repulsive cost. We point out that our construction can deal with the case when the space X is a domain in \({\mathbb {R}}^d\), answering a question raised in Benamou et al. (Numer Math 142:33–54, 2019). Finally, we also prove the entropy-regularized version of the Kantorovich duality.

中文翻译：

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具有排斥成本的多边际熵传输

在本文中，我们研究了带有排斥成本函数的熵传递函数的理论性质。我们为一类度量空间中的极小值的存在提供了充分的条件，并证明了排斥性的熵传输函数对多边际最优传输问题的\（\ Gamma \）收敛性。我们指出，当空间X是\（{\ mathbb {R}} ^ d \）中的一个域时，我们的构造可以处理这种情况，回答Benamou等人提出的问题。（数字数学142：33–54，2019）。最后，我们还证明了Kantorovich对偶的熵正则化形式。