# Optimisation approach for the Monge-Ampere equation

## TL;DR

This paper introduces an optimization-based numerical method for solving the Monge-Ampere equation, reformulating it as a functional minimization problem and demonstrating effective approximations through finite element methods.

## Contribution

It proposes a novel approach that reformulates the Monge-Ampere equation as an optimization problem solved via finite element methods, providing a new computational technique.

## Key findings

- Good approximation achieved in 68 iterations
- Reformulation as an optimization problem is effective
- Finite element Galerkin method successfully applied

## 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.