Volume 25, 2019
|Number of page(s)||54|
|Published online||26 July 2019|
Dynamic models of Wasserstein-1-type unbalanced transport
Applied Mathematics: Institute for Analysis and Numerics, University of Muenster,
* Corresponding author: firstname.lastname@example.org
Accepted: 2 March 2018
We consider a class of convex optimization problems modelling temporal mass transport and mass change between two given mass distributions (the so-called dynamic formulation of unbalanced transport), where we focus on those models for which transport costs are proportional to transport distance. For those models we derive an equivalent, computationally more efficient static formulation, we perform a detailed analysis of the model optimizers and the associated optimal mass change and transport, and we examine which static models are generated by a corresponding equivalent dynamic one. Alongside we discuss thoroughly how the employed model formulations relate to other formulations found in the literature.
Mathematics Subject Classification: 49K15 / 37N40
Key words: Wasserstein distance / unbalanced transport / convex optimization
© EDP Sciences, SMAI 2019
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