Efficient Numerical Methods for Solving a Class of Non-Potential Mean-Field Games

The authors propose a monotone splitting algorithm for solving a class of second-order non-potential mean-field games, where the finite-difference scheme represents first-order optimality conditions for a primal-dual pair of monotone inclusions. They prove that the finite-difference system obtains a solution that can be provably recovered by an extension of the primal-dual hybrid gradient (PDHG) algorithm.