We prove the convergence of a damped Newton's method for the nonlinear system resulting from a discretization of the second boundary value problem for the Monge-Ampere equation. The boundary condition is enforced through the use of the notion of asymptotic cone. The differential operator is discretized based on a discrete analogue of the subdifferential.

翻译：本文证明了针对离散化Monge-Ampère方程第二边值问题所得非线性方程组的阻尼牛顿法的收敛性。边界条件通过渐近锥概念进行约束，微分算子则基于次微分的离散模拟进行离散化处理。