Abstract: 

In this talk, we aim to introduce an HPR-LP solver, an implementation of a Halpern Peaceman-Rachford (HPR) method with semi-proximal terms for solving linear programming (LP).  We start with showing that the HPR method enjoys the highly desired iteration complexity of O(1/k) in terms of the Karush-Kuhn-Tucker residual and the objective error via the theory developed recently for accelerated degenerate proximal point methods. Based on the complexity results, we then design an adaptive strategy of restart and penalty parameter update to improve the efficiency and robustness of the HPR method. We conduct extensive numerical experiments on different LP benchmark datasets using NVIDIA A100-SXM4-80GB GPU in different stopping tolerances. Our solver's Julia version achieves a 2.39x to 5.70x speedup measured by SGM10 on benchmark datasets with presolve (2.03x to 4.06x without presolve) over the award-winning solver PDLP with the tolerance of 10^{-8}. Several practical techniques underlining the efficiency of the HPR-LP solver will be highlighted.   

个人简介：

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，美国工业与应用数学学会会士，中国工业与应用数学学会会士，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，现任国际顶级数学期刊《Mathematical Programming(数学规划)》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杰出合作奖。  2022 年获香港研资局高级研究学者奖。2024年当选中国运筹学会会士。