An efficient second-order cone programming approach for dynamic optimal transport on staggered grid discretization

Liang Chen; Youyicun Lin; Yuxuan Zhou

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arXiv · 2505.05424

An efficient second-order cone programming approach for dynamic optimal transport on staggered grid discretization

Liang Chen·Youyicun Lin·Yuxuan Zhou

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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.

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BibTeX RIS

Liang Chen, Youyicun Lin, Yuxuan Zhou. 2025-05-08. An efficient second-order cone programming approach for dynamic optimal transport on staggered grid discretization. https://arxiv.org/abs/2505.05424

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