{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/an-efficient-second-order-cone-programming-1","title":"An efficient second-order cone programming approach for dynamic optimal transport on staggered grid discretization","arxiv_id":"2505.05424","date":"2025-05-08","proceeding":null,"authors":["Liang Chen","Youyicun Lin","Yuxuan Zhou"],"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.","url_abs":"https://arxiv.org/abs/2505.05424v1","url_pdf":"https://arxiv.org/pdf/2505.05424v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"an-efficient-second-order-cone-programming-1","repo_url":"https://github.com/chlhnu/dot-socp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}