Monge-Kantorovich interpolation with constraints and application to a parking problem
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arXiv
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| Format: | Preprint |
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2022
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| author | Buttazzo, Giuseppe Carlier, Guillaume Eichinger, Katharina |
| author_facet | Buttazzo, Giuseppe Carlier, Guillaume Eichinger, Katharina |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_14261 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Monge-Kantorovich interpolation with constraints and application to a parking problem Buttazzo, Giuseppe Carlier, Guillaume Eichinger, Katharina Optimization and Control 49Q22, 49J45, 49M29, 49K99 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. |
| title | Monge-Kantorovich interpolation with constraints and application to a parking problem |
| topic | Optimization and Control 49Q22, 49J45, 49M29, 49K99 |
| url | https://arxiv.org/abs/2207.14261 |