{"ID":2864349,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.23903","arxiv_id":"2509.23903","title":"On the Relationships among GPU-Accelerated First-Order Methods for Solving Linear Programming","abstract":"This paper aims to understand the relationships among recently developed GPU-accelerated first-order methods (FOMs) for linear programming (LP), with particular emphasis on HPR-LP -- a Halpern Peaceman--Rachford (HPR) method for LP. Our findings can be summarized as follows: (i) the base algorithm of cuPDLPx, a recently released GPU solver, is a special case of the base algorithm of HPR-LP, thereby showing that cuPDLPx is another concrete implementation instance of HPR-LP; (ii) once the active sets have been identified, HPR-LP and EPR-LP -- an ergodic PR method for LP -- become equivalent under the same initialization; and (iii) extensive numerical experiments on benchmark datasets demonstrate that HPR-LP achieves the best overall performance among current GPU-accelerated LP solvers. These findings provide a strong motivation for using the HPR method as a baseline to further develop GPU-accelerated LP solvers and beyond.","short_abstract":"This paper aims to understand the relationships among recently developed GPU-accelerated first-order methods (FOMs) for linear programming (LP), with particular emphasis on HPR-LP -- a Halpern Peaceman--Rachford (HPR) method for LP. Our findings can be summarized as follows: (i) the base algorithm of cuPDLPx, a recentl...","url_abs":"https://arxiv.org/abs/2509.23903","url_pdf":"https://arxiv.org/pdf/2509.23903v2","authors":"[\"Kaihuang Chen\",\"Defeng Sun\",\"Yancheng Yuan\",\"Guojun Zhang\",\"Xinyuan Zhao\"]","published":"2025-09-28T14:20:02Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}