School of Mathematical Sciences, Shenzhen University  

Liyuan Scholar Colloquium No. 148  

Lecture Title: A GPU based Halpern Peaceman–Rachford method for solving convex programming  

Speaker: Professor Sun Defeng (The Hong Kong Polytechnic University)  

Lecture Time: October 20, 2025, 16:30-17:30 (afternoon)  

Venue: Classroom 1, Huixing Building, Yuehai Campus, Shenzhen University  

Abstract:  

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.]

Lecturer’s Biography:  

Sun Defeng is Head of the Department of Applied Mathematics and Chair Professor of Applied Optimization and Operations Research at The Hong Kong Polytechnic University. He is a Fellow of the Society for Industrial and Applied Mathematics (SIAM, USA) and a Fellow of the Chinese Society for Industrial and Applied Mathematics (CSIAM), and served as the former President of the Hong Kong Mathematical Society. He has received prestigious awards including the 2018 Beale–Orchard-Hays Prize in International Mathematical Programming and the First Outstanding Scientist Award of the Faculty of Science, National University of Singapore. He previously served as Editor-in-Chief of the Asia-Pacific Journal of Operational Research and currently holds positions as Associate Editor of Mathematical Programming and SIAM Journal on Optimization.   Professor Sun has published over 100 academic papers in top international optimization journals such as Mathematics of Operations Research, Mathematical Programming, and SIAM Journal on Optimization. His research focuses on continuous optimization and machine learning, covering fundamental theory, algorithms, and applications. He has profound expertise in semismooth and smoothing Newton methods, as well as linear and nonlinear matrix optimization. His series of achievements in asymmetric matrix optimization problems have laid the foundation for the new research direction of matrix optimization. In 2021, he received Outstanding Cooperation Awards from Huawei Hong Kong Research Center and Noah's Ark Laboratory respectively for his contributions to optimization solvers for scheduling. In 2022, he was awarded the Senior Research Fellow Award from the Research Grants Council of Hong Kong. In 2024, he was elected as a Fellow of the Operations Research Society of China.  

Faculty and students are welcome to attend!  

School of Mathematical Sciences  

October 16, 2025