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In this paper, we propose a monotone mixed finite difference scheme for solving the two-dimensional Monge–Ampère equation. In order to accomplish this, we convert the Monge–Ampère equation to an equivalent Hamilton–Jacobi–Bellman (HJB) equation. Based on the HJB formulation, we apply the standard 7-point stencil discretization, which is second order accurate, to the grid points wherever monotonicity...