An iterative scheme for solving the optimal transportation problem
This work offers a theoretical guarantee for an iterative method in optimal transport, but the contribution is incremental as it builds on existing approaches.
The authors propose an iterative scheme for approximating the optimal transportation problem with a discrete target measure, providing a finite upper bound on iterations needed based on error tolerance and support size.
We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Additionally, we give a finite upper bound on the number of iterations necessary for the scheme to terminate, in terms of the error tolerance and number of points in the support of the discrete target measure.