An iterative scheme for solving the optimal transportation problem

TL;DR

This paper introduces an iterative method to approximate the optimal transportation problem with discrete targets, providing a finite bound on iterations needed for convergence based on error tolerance and support size.

Contribution

The paper presents a novel iterative scheme for solving the optimal transportation problem with discrete targets and establishes a finite iteration bound for convergence.

Findings

Iterative scheme effectively approximates the optimal transportation problem.

Finite upper bound on iterations depends on error tolerance and support size.

Scheme converges under standard cost function conditions.

Abstract

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.