This paper proposes a multiscale method for solving the numerical solution of mean field games which accelerates convergence and addresses problem determining initial guess. Starting from an approximate at coarsest level, constructs approximations on successively finer grids via alternating sweeping, not only allows use classical time marching schemes, but also enables applications to both loca...

We propose a modified extragradient method for solving the variational inequality problem in Hilbert space. The is combination of well-known subgradient with Mann’s mean value which updated iterate picked convex hull all previous iterates. show weak convergence to solution problem, provided that condition on corresponding averaging matrix fulfilled. Some numerical experiments are given effectiv...