报告题目：Algorithm for Financial Engineering: A GPU implementation of HPR for solving linear programming and convex composite quadratic programming

报告人：孙德锋教授(香港理工大学)

时间：2025年9月29日上午10:00-11:30

地点：性爱直播 创新港涵英楼5-8001会议室

报告人简介：

孙德锋教授现任香港理工大学应用优化与运筹学讲座教授，香港理工大学金融科技硕士项目负责人。他的研究主要集中在非凸连续优化和机器学习以及金融科技。并在相关领域发表了大量成果。获得2018年度三年一度的Beale–Orchard-Hays奖。他于2011年至2013年担任《亚太运筹学杂志》主编，目前担任《Mathematical Programming》、《SIAM Journal on Optimization》、《Journal of Optimization Theory and Applications》、《Journal of the Operations Research Society of China》、《Journal of Computational Mathematics》以及《Science China: Mathematics》的副主编。2020年，他当选为CSIAM和SIAM会士；2021年，他因在开发高效且稳健的优化技术方面的贡献，尤其是这些技术在金融建模与金融工程应用中的重要作用，而获得香港研究中心和华为诺亚方舟实验室颁发的杰出合作奖。

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 a desired convergence rate. Subsequently, building upon the accelerated dPPM, we develop an accelerated pADMM algorithm that exhibits an nonergodic convergence rate 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.