Geodesic
Monge–Kantorovich interpolation with constraints and application to a parking problem
Giuseppe Buttazzo1 ; Guillaume Carlier2 ; Katharina Eichinger3
1Università di Pisa, Italy
2Université Paris Dauphine-PSL, Paris Cedex 16, France; Inria, Paris, France
3École Polytechnique, Palaiseau Cedex, France
Interfaces and free boundaries, Tome 26 (2024) no. 2, pp. 283-320

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DOI

We consider optimal transport problems where the cost for transporting a given probability measure μ0​ to another one (μ1​) consists of two parts: the first one measures the transportation from μ0​ to an intermediate (pivot) measure μ to be determined (and subject to various constraints), and the second one measures the transportation from μ to μ1​. 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.
DOI : 10.4171/ifb/514
Classification : 49Q22, 49J45, 49M29, 49K99
Mots-clés : optimal transport, Monge–Kantorovich distance, measure interpolation, optimal parking regions

Giuseppe Buttazzo  1   ; Guillaume Carlier  2   ; Katharina Eichinger  3

1 Università di Pisa, Italy
2 Université Paris Dauphine-PSL, Paris Cedex 16, France; Inria, Paris, France
3 École Polytechnique, Palaiseau Cedex, France 
Giuseppe Buttazzo; Guillaume Carlier; Katharina Eichinger. Monge–Kantorovich interpolation with constraints and application to a parking problem. Interfaces and free boundaries, Tome 26 (2024) no. 2, pp. 283-320. doi: 10.4171/ifb/514
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     author = {Giuseppe Buttazzo and Guillaume Carlier and Katharina Eichinger},
     title = {Monge{\textendash}Kantorovich interpolation with constraints and application to a parking problem},
     journal = {Interfaces and free boundaries},
     pages = {283--320},
     year = {2024},
     volume = {26},
     number = {2},
     doi = {10.4171/ifb/514},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/514/}
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