Monotone inclusion methods for a class of second-order non-potential mean-field games
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914734343716864 |
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| author | Nurbekyan, Levon Liu, Siting Chow, Yat Tin |
| author_facet | Nurbekyan, Levon Liu, Siting Chow, Yat Tin |
| contents | We propose a monotone splitting algorithm for solving a class of second-order non-potential mean-field games. Following [Achdou, Capuzzo-Dolcetta, "Mean Field Games: Numerical Methods," SINUM (2010)], we introduce a finite-difference scheme and observe that the scheme represents first-order optimality conditions for a primal-dual pair of monotone inclusions. Based on this observation, we prove that the finite-difference system obtains a solution that can be provably recovered by an extension of the celebrated primal-dual hybrid gradient (PDHG) algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_20290 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monotone inclusion methods for a class of second-order non-potential mean-field games Nurbekyan, Levon Liu, Siting Chow, Yat Tin Optimization and Control Numerical Analysis Primary, 35Q89, 65M06, 35A15, 49N80, Secondary, 35Q91, 35Q93, 91A16, 93A15, 93A16 We propose a monotone splitting algorithm for solving a class of second-order non-potential mean-field games. Following [Achdou, Capuzzo-Dolcetta, "Mean Field Games: Numerical Methods," SINUM (2010)], we introduce a finite-difference scheme and observe that the scheme represents first-order optimality conditions for a primal-dual pair of monotone inclusions. Based on this observation, we prove that the finite-difference system obtains a solution that can be provably recovered by an extension of the celebrated primal-dual hybrid gradient (PDHG) algorithm. |
| title | Monotone inclusion methods for a class of second-order non-potential mean-field games |
| topic | Optimization and Control Numerical Analysis Primary, 35Q89, 65M06, 35A15, 49N80, Secondary, 35Q91, 35Q93, 91A16, 93A15, 93A16 |
| url | https://arxiv.org/abs/2403.20290 |