论文标题
Monge-Kantorovich插值，限制和应用于停车问题
Monge-Kantorovich interpolation with constraints and application to a parking problem
论文作者
论文摘要
我们考虑最佳的运输问题，在其中运输给定概率度量的成本$μ_0$ $μ__1$由两个部分组成：第一个零件衡量从$μ_0$到中间（pivot）$μ$的运输量，要确定（并受到各种约束），第二个衡量了$ $ $ $ $ $μ_1的运输。这导致在约束下的Monge-Kantorovich插值问题，我们为此建立了最佳枢轴测量$μ$的各种特性。考虑到更普遍的情况，只有群众只使用中间停止才能为城市周围停车区的最佳位置提供数学模型。基于熵正则化的数值模拟既针对最佳停车区，也针对Monge-Kantorovich限制了插值问题。
We consider optimal transport problems where the cost for transporting a given probability measure $μ_0$ to another one $μ_1$ consists of two parts: the first one measures the transportation from $μ_0$ to an intermediate (pivot) measure $μ$ to be determined (and subject to various constraints), and the second one measures the transportation from $μ$ to $μ_1$. This leads to Monge-Kantorovich interpolation problems under constraints for which we establish various properties of the optimal pivot measures $μ$. Considering the more general situation where only some part of the mass uses the intermediate stop leads to a mathematical model for the optimal location of a parking region around a city. Numerical simulations, based on entropic regularization, are presented both for the optimal parking regions and for Monge-Kantorovich constrained interpolation problems.
