| Abstract: |
| We address the numerical approximation of Mean Field Games with local couplings. For power-like Hamiltonians, we consider both unconstrained and constrained stationary systems with density constraints in order to model hard congestion effects. For finite difference discretizations of the Mean Field Game system, we follow a variational approach. We prove that the aforementioned schemes can be obtained as the optimality system of suitably defined optimization problems. Next, assuming next that the coupling term is monotone, we study and compare several proximal type globally convergent first-order methods for solving the convex optimization problems. Each step of the proposed algorithms is easy computable, which leads to efficient implementations. |
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