Fourier approximation methods for first-order nonlocal mean-field games
Levon NurbekyanMcGill University, Montreal, Canada
João SaúdeCarnegie Mellon University, Pittsburgh, USA
In this note, we develop Fourier approximation methods for the solutions of first-order nonlocal mean-field games (MFG) systems. Using Fourier expansion techniques, we approximate a given MFG system by a simpler one that is equivalent to a convex optimization problem over a finite-dimensional subspace of continuous curves. Furthermore, we perform a time-discretization for this optimization problem and arrive at a finite-dimensional saddle point problem. Finally, we solve this saddle-point problem by a variant of a primal dual hybrid gradient method.
Cite this article
Levon Nurbekyan, João Saúde, Fourier approximation methods for first-order nonlocal mean-field games. Port. Math. 75 (2018), no. 3/4, pp. 367–396DOI 10.4171/PM/2023