A semi-Lagrangian scheme for First-Order Mean Field Games based on monotone operators
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909032035385344 |
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| author | Carlini, Elisabetta Coscetti, Valentina |
| author_facet | Carlini, Elisabetta Coscetti, Valentina |
| contents | We construct a semi-Lagrangian scheme for first-order, time-dependent, and non-local Mean Field Games. The convergence of the scheme to a weak solution of the system is analyzed by exploiting a key monotonicity property. To solve the resulting discrete problem, we implement a Learning Value Algorithm, prove its convergence, and propose an acceleration strategy based on a Policy iteration method. Finally, we present numerical experiments that validate the effectiveness of the proposed schemes and show that the accelerated version significantly improves performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10509 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A semi-Lagrangian scheme for First-Order Mean Field Games based on monotone operators Carlini, Elisabetta Coscetti, Valentina Numerical Analysis 91A16, 49N80, 35Q89, 65M12, 65M25 We construct a semi-Lagrangian scheme for first-order, time-dependent, and non-local Mean Field Games. The convergence of the scheme to a weak solution of the system is analyzed by exploiting a key monotonicity property. To solve the resulting discrete problem, we implement a Learning Value Algorithm, prove its convergence, and propose an acceleration strategy based on a Policy iteration method. Finally, we present numerical experiments that validate the effectiveness of the proposed schemes and show that the accelerated version significantly improves performance. |
| title | A semi-Lagrangian scheme for First-Order Mean Field Games based on monotone operators |
| topic | Numerical Analysis 91A16, 49N80, 35Q89, 65M12, 65M25 |
| url | https://arxiv.org/abs/2506.10509 |