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

A regularized Interior Point Method for sparse Optimal Transport on Graphs