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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.05416 |
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| _version_ | 1866914718921261056 |
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| author | Camilli, Fabio Tang, Qing |
| author_facet | Camilli, Fabio Tang, Qing |
| contents | We analyze asymptotic convergence properties of Newton's method for a class of evolutive Mean Field Games systems with non-separable Hamiltonian arising in mean field type models with congestion. We prove the well posedness of the Mean Field Game system with non-separable Hamiltonian and of the linear system giving the Newton iterations. Then, by forward induction and assuming that the initial guess is sufficiently close to the solution of problem, we show a quadratic rate of convergence for the approximation of the Mean Field Game system by Newton's method. We also consider the case of a nonlocal coupling, but with separable Hamiltonian, and we show a similar rate of convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05416 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the quadratic convergence of Newton's method for Mean Field Games with non-separable Hamiltonian Camilli, Fabio Tang, Qing Optimization and Control Analysis of PDEs 49N70, 91A13, 35Q80, 65M12 We analyze asymptotic convergence properties of Newton's method for a class of evolutive Mean Field Games systems with non-separable Hamiltonian arising in mean field type models with congestion. We prove the well posedness of the Mean Field Game system with non-separable Hamiltonian and of the linear system giving the Newton iterations. Then, by forward induction and assuming that the initial guess is sufficiently close to the solution of problem, we show a quadratic rate of convergence for the approximation of the Mean Field Game system by Newton's method. We also consider the case of a nonlocal coupling, but with separable Hamiltonian, and we show a similar rate of convergence. |
| title | On the quadratic convergence of Newton's method for Mean Field Games with non-separable Hamiltonian |
| topic | Optimization and Control Analysis of PDEs 49N70, 91A13, 35Q80, 65M12 |
| url | https://arxiv.org/abs/2311.05416 |