Proximal methods for stationary Mean Field Games with local couplings

Understand

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.