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

11/01/2019

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by   Gerard Awanou, et al.

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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. For the differential operator we use a discretization which is based on a partial discrete analogue of the subdifferential.