Convergence of a damped Newton's method for discrete Monge-Ampere functions with a prescribed asymptotic cone

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 partial discrete analogue of the subdifferential.