An efficient second-order cone programming approach for dynamic optimal transport on staggered grid discretization
Abstract
This paper proposes an efficient numerical method based on second-order cone programming (SOCP) to solve dynamic optimal transport (DOT) problems with quadratic cost on staggered grid discretization. By properly reformulating discretized DOT problems into a linear SOCP, the proposed method eliminates the interpolation matrices and thus avoids solving a series of cubic equations and linear systems induced by interpolation. Then, by taking advantage of the SOCP reformulation, we can solve them efficiently by a computationally highly economical implementation of an inexact decomposition-based proximal augmented Lagrangian method. Moreover, we have made the proposed approach an open-source software package. Numerical experiments on various DOT problems suggest that the proposed approach performs significantly more efficiently than state-of-the-art software packages. In addition, it exhibits prominent robustness to problems with non-negative measures.
Cite
@article{arxiv.2505.05424,
title = {An efficient second-order cone programming approach for dynamic optimal transport on staggered grid discretization},
author = {Liang Chen and Youyicun Lin and Yuxuan Zhou},
journal= {arXiv preprint arXiv:2505.05424},
year = {2026}
}