Unnormalized optimal transport
Unnormalized optimal transport
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DOI：
10.1016/j.jcp.2019.108940
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发表时间：
2019-12-15
影响因子：
4.1
通讯作者：
Puthawala, Michael
中科院分区：
文献类型：
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作者：
Gangbo, Wilfrid;Li, Wuchen;Puthawala, Michael
我们提出了计算流体力学方法的Monge-Kantorovich质量传递问题，这是由Benamou-Brenier在[4]中开发的扩展。我们的扩展允许非归一化和不平等的质量的最佳转移。我们得到了[4]中公式的一个单参数简单修正族。这使我们得到一个新的Monge-Ampere型方程和一个新的Kantorovich对偶公式。这些可以通过例如Chambolle-Pock原始-对偶算法有效地解决[6]。这个扩展传质问题的解决方案为我们提供了一个简单的度量，用于计算两个非归一化密度之间的距离。在[25]（这是我们在这里工作的先驱）中，这个度量的L-1版本具有理想的性质。(C)2019爱思唯尔公司All rights reserved.
We propose an extension of the computational fluid mechanics approach to the Monge-Kantorovich mass transfer problem, which was developed by Benamou-Brenier in [4]. Our extension allows optimal transfer of unnormalized and unequal masses. We obtain a oneparameter family of simple modifications of the formulation in [4]. This leads us to a new Monge-Ampere type equation and a new Kantorovich duality formula. These can be solved efficiently by, for example, the Chambolle-Pock primal-dual algorithm [6]. This solution to the extended mass transfer problem gives us a simple metric for computing the distance between two unnormalized densities. The L-1 version of this metric was shown in [25] (which is a precursor of our work here) to have desirable properties. (C) 2019 Elsevier Inc. All rights reserved.