国产探花

荔园学者Colloquium第一百四十八期

讲座题目: A GPU based Halpern Peaceman–Rachford method for solving convex programming

主讲人： 孙德锋 教授（香港理工大学）

讲座时间：2025年10月20日下午16：30-17：30

讲座地点：深圳大学粤海校区汇星楼一号教室

内容摘要：We aim to employ an accelerated preconditioned alternating direction method of multipliers (pADMM), whose proximal terms are convex quadratic functions, to solve linearly constrained convex optimization problems. To achieve this, we first reformulate the pADMM into a form of proximal point method (PPM) with a positive semidefinite preconditioner which can be degenerate due to the lack of strong convexity of the proximal terms in the pADMM. Then we accelerate the pADMM by accelerating the reformulated degenerate PPM (dPPM). Specifically, we first propose an accelerated dPPM by integrating the Halpern iteration into it, achieving non-asymptotic O(1/k) convergence rates. Subsequently, building upon the accelerated dPPM, we develop an accelerated pADMM algorithm that exhibits the non-asymptotic O(1/k)  nonergodic convergence rates in terms of the real stopping criteria-- the Karush–Kuhn–Tucker residual and the primal objective function value gap. Extensive numerical experiments on large-scale linear programming and convex composite quadratic programming  benchmark datasets, conducted using a GPU, demonstrate the substantial advantages of our Halpern Peaceman–Rachford (HPR) method—a special case of the Halpern-accelerated pADMM framework applied to the dual problems—over state-of-the-art solvers, including the award-winning PDLP, as well as PDQP, SCS, CuClarabel, and Gurobi, in achieving high-accuracy solutions.  [This talk is based on joint papers with Kaihuang Chen, Yancheng Yuan, Guojun Zhang, and Xinyuan Zhao.]

主讲人简介：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《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。2024年当选中国运筹学会会士。

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　　　　　　　　　　　　　　　　　　　　2025年10月16日