An augmented Lagrangian approach to Wasserstein gradient flows and applications
Taking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we propose a convex formulation for each step of the JKO scheme for Wasserstein gradient flows which can be attacked by an augmented Lagrangian method which we call the ALG2-JKO scheme. We test the algorithm in particu...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2016-06-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | https://doi.org/10.1051/proc/201654001 |
| _version_ | 1797971391620841472 |
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| author | Benamou Jean-David Carlier Guillaume Laborde Maxime |
| author_facet | Benamou Jean-David Carlier Guillaume Laborde Maxime |
| author_sort | Benamou Jean-David |
| collection | DOAJ |
| description | Taking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we propose a convex formulation for each step of the JKO scheme for Wasserstein gradient flows which can be attacked by an augmented Lagrangian method which we call the ALG2-JKO scheme. We test the algorithm in particular on the porous medium equation. We also consider a semi implicit variant which enables us to treat nonlocal interactions as well as systems of interacting species. Regarding systems, we can also use the ALG2-JKO scheme for the simulation of crowd motion models with several species. |
| first_indexed | 2024-04-11T03:31:55Z |
| format | Article |
| id | doaj.art-05613afd315644ecb652a02fc8ae9898 |
| institution | Directory Open Access Journal |
| issn | 2267-3059 |
| language | English |
| last_indexed | 2024-04-11T03:31:55Z |
| publishDate | 2016-06-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj.art-05613afd315644ecb652a02fc8ae98982023-01-02T06:08:13ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592016-06-015411710.1051/proc/201654001proc165401An augmented Lagrangian approach to Wasserstein gradient flows and applicationsBenamou Jean-DavidCarlier GuillaumeLaborde MaximeTaking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we propose a convex formulation for each step of the JKO scheme for Wasserstein gradient flows which can be attacked by an augmented Lagrangian method which we call the ALG2-JKO scheme. We test the algorithm in particular on the porous medium equation. We also consider a semi implicit variant which enables us to treat nonlocal interactions as well as systems of interacting species. Regarding systems, we can also use the ALG2-JKO scheme for the simulation of crowd motion models with several species.https://doi.org/10.1051/proc/201654001 |
| spellingShingle | Benamou Jean-David Carlier Guillaume Laborde Maxime An augmented Lagrangian approach to Wasserstein gradient flows and applications ESAIM: Proceedings and Surveys |
| title | An augmented Lagrangian approach to Wasserstein gradient flows and applications |
| title_full | An augmented Lagrangian approach to Wasserstein gradient flows and applications |
| title_fullStr | An augmented Lagrangian approach to Wasserstein gradient flows and applications |
| title_full_unstemmed | An augmented Lagrangian approach to Wasserstein gradient flows and applications |
| title_short | An augmented Lagrangian approach to Wasserstein gradient flows and applications |
| title_sort | augmented lagrangian approach to wasserstein gradient flows and applications |
| url | https://doi.org/10.1051/proc/201654001 |
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