HPR Solver Family: Open-Source GPU-Accelerated First-Order Solvers for Large-Scale Optimization

报告摘要：The growing scale of modern optimization problems creates increasing demand for high-performance solvers that can harness modern GPU architectures. In this talk, we introduce the Halpern Peaceman–Rachford (HPR) method, a GPU-friendly accelerated splitting method for convex optimization. HPR achieves an $O(1/k)$ convergence rate in terms of the Karush–Kuhn–Tucker residual from the best possible $O(1/\sqrt{k})$ rate of its unaccelerated counterpart. Building on this theoretical advancement, we develop the HPR Solver Family, a suite of open-source, GPU-accelerated first-order solvers for large-scale optimization. In particular, the linear programming (LP) solver HPR-LP incorporates a number of practical techniques, including GPU-native presolving, adaptive restarting, sieving to exploit solution sparsity, and structure-aware sparse matrix–vector multiplication (SpMV). On the Mittelmann LPfeas benchmark (September 16, 2026), HPR-LP ranks first on both the main benchmark set and the addendum and is the only solver to solve all 13 addendum instances, including problems with hundreds of millions of variables and over one billion nonzeros. Beyond LP, the family includes HPR-QP for convex quadratic programming, HPR-SOCP for second-order cone programming, and HOT for large-scale optimal transport. Together, these developments form an expanding GPU-native optimization ecosystem, with ongoing work extending it to broader classes of large-scale structured optimization problems arising in machine learning, operations research, and scientific computing.

报告人简介：孙德锋，香港理工大学应用数学系系主任和应用优化与运筹学讲座教授，美国数学学会会士，美国工业与应用数学学会会士，中国工业与应用数学学会会士，中国运筹学会会士, 香港数学学会前任会长。荣获2018国际数学规划Beale--Orchard-Hays奖及新加坡国立大学科学学院首届杰出科学家奖。曾任《Asia-Pacific Journal of Operational Research（亚太运筹学杂志）》主编，现任《Mathematical Programming》编委，《SIAM Journal on Optimization》编委等。在Mathematics of Operations Research, Mathematical Programming, SIAM Journal on Optimization等国际权威优化刊物上发表学术论文百余篇。主要从事连续优化及机器学习的研究，包括基础理论、算法及应用。在半光滑和光滑化牛顿方法，以及线性和非线性矩阵优化等方面具有很深造诣。其在非对称矩阵优化问题方面取得的系列成果促成了矩阵优化这一新研究方向。 2021年凭借排产方面优化求解器的贡献， 获得华为香港研究所和诺亚方舟实验室分别颁发杰出合作奖。 2022 年获香港研资局高级研究学者奖。