Title: Optimisation approach for the Monge-Ampere equation,
Abstract: This paper studies the numerical approximation of solution of the Dirichlet
problem for the fully nonlinear Monge-Ampere equation. In this approach, we
take the advantage of reformulation the Monge-Ampere problem as an optimization
problem, to which we associate a well defined functional whose minimum provides
us with the solution to the Monge-Ampere problem after resolving a Poisson
problem by the finite element Galerkin method. We present some numerical
examples, for which a good approximation is obtained in 68 iterations.