Dynamic Optimal Transport on Networks

被引：1

作者：

Burger, Martin ^{[1
]}

Humpert, Ina ^{[2
]}

Pietschmann, Jan-Frederik ^{[3
]}

机构：

[1] Deutsch Elektronen Synchrotron DESY, Computat Imaging Grp & Helmholtz Imaging, Hamburg, Germany

[2] Westfal Wilhelms Univ WWU Munster, Inst Anal & Computat Math, Munster, Germany

[3] Univ Augsburg, Inst Math, MNTF, Augsburg, Germany

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2023年 / 29卷

关键词：

Metric graph; optimal transport; gradient flow; convex duality; entropy; HELLINGER-KANTOROVICH DISTANCE; EQUATIONS;

D O I：

10.1051/cocv/2023027

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We study a dynamic optimal transport problem on a network. Despite the cost for transport along the edges, an additional cost, scaled with a parameter & kappa;, has to be paid for interchanging mass between edges and vertices. We show existence of minimisers using duality and discuss the relationship of the model to other metrics such as Fisher-Rao and the classical Wasserstein metric. Finally, we examine the limiting behaviour of the model in terms of the parameter & kappa;.

引用

页数：23

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