Newton Methods for Mean Field Games: A Numerical Study
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914409092218880 |
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| author | Carlini, Elisabetta Zorkot, Ahmad |
| author_facet | Carlini, Elisabetta Zorkot, Ahmad |
| contents | We address the numerical solution of second-order Mean Field Game problems through Newton iterations in infinite dimensions, introduced in [14], where quadratic convergence of the method was rigorously established. Building upon this theoretical framework, we develop new numerical discretization techniques, including both a finite difference and a semi-Lagrangian scheme, that enable an effective computational implementation of the infinite-dimensional iterations.
The proposed methods are tested on several benchmark problems, and the resulting numerical experiments demonstrate their robustness, accuracy, and efficiency. A comparative analysis between the two schemes and existing approaches from the literature is also presented, highlighting the potential of Newton-based solvers for MFG systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12752 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Newton Methods for Mean Field Games: A Numerical Study Carlini, Elisabetta Zorkot, Ahmad Numerical Analysis Analysis of PDEs 91A16 (Primary), 35K55, 49L20, 65M06, 65M12 (Secondary) We address the numerical solution of second-order Mean Field Game problems through Newton iterations in infinite dimensions, introduced in [14], where quadratic convergence of the method was rigorously established. Building upon this theoretical framework, we develop new numerical discretization techniques, including both a finite difference and a semi-Lagrangian scheme, that enable an effective computational implementation of the infinite-dimensional iterations. The proposed methods are tested on several benchmark problems, and the resulting numerical experiments demonstrate their robustness, accuracy, and efficiency. A comparative analysis between the two schemes and existing approaches from the literature is also presented, highlighting the potential of Newton-based solvers for MFG systems. |
| title | Newton Methods for Mean Field Games: A Numerical Study |
| topic | Numerical Analysis Analysis of PDEs 91A16 (Primary), 35K55, 49L20, 65M06, 65M12 (Secondary) |
| url | https://arxiv.org/abs/2512.12752 |