In this work we propose a discretization of the second boundary condition for the Monge-Ampere equation arising in geometric optics and optimal transport. The discretization we propose is the natural generalization of the popular Oliker-Prussner method proposed in 1988. For the discretization of the differential operator, we use a discrete analogue of the subdifferential. Existence, unicity and stability of the solutions to the discrete problem are established. Convergence results to the continuous problem are given.

翻译：本文针对几何光学和最优传输中出现的Monge-Ampere方程的第二边界条件提出了一种离散化方法。所提出的离散化是1988年提出的经典Oliker-Prussner方法的自然推广。对于微分算子的离散化，我们采用了次微分的离散模拟。文中建立了离散问题解的存在性、唯一性和稳定性，并给出了其向连续问题收敛的结果。