A regularized Interior Point Method for sparse Optimal Transport on Graphs

TL;DR

This paper introduces a regularized Interior Point Method tailored for large-scale sparse Optimal Transport problems on graphs, enhancing scalability and efficiency through primal-dual regularization and sparsified Newton equations.

Contribution

The paper develops a novel regularized IPM that exploits primal-dual regularization to efficiently solve large sparse OT problems on graphs, with proven polynomial convergence.

Findings

Demonstrates improved efficiency over network simplex solvers.

Shows robustness and scalability on large sparse graphs.

Provides theoretical convergence guarantees.

Abstract

In this work, the authors address the Optimal Transport (OT) problem on graphs using a proximal stabilized Interior Point Method (IPM). In particular, strongly leveraging on the induced primal-dual regularization, the authors propose to solve large scale OT problems on sparse graphs using a bespoke IPM algorithm able to suitably exploit primal-dual regularization in order to enforce scalability. Indeed, the authors prove that the introduction of the regularization allows to use sparsified versions of the normal Newton equations to inexpensively generate IPM search directions. A detailed theoretical analysis is carried out showing the polynomial convergence of the inner algorithm in the proposed computational framework. Moreover, the presented numerical results showcase the efficiency and robustness of the proposed approach when compared to network simplex solvers.