报告题目：Restarted Primal-Dual Hybrid Conjugate Gradient Method for Large-Scale Quadratic Programming

报告人：刘慧康，上海交通大学 安泰经济与管理学院

报告时间：7月5日 10:30

报告地点：管理楼1308

摘要：

Convex quadratic programming (QP) is an essential class of optimization problems with broad applications across various fields. Traditional QP solvers, typically based on simplex or barrier methods, face significant scalability challenges . In response to these limitations, recent research has shifted towards matrix-free first order methods to enhance scalability in QP. Among these, the restarted accelerated primal-dual hybrid gradient (rAPDHG) method has gained notable attention due to its linear convergence rate to an optimal solution and its straightforward implementation on Graphics Processing Units (GPUs). Building on this framework, this paper introduces a restarted primal-dual hybrid conjugate gradient (PDHCG) method, which incorporates conjugate gradient (CG) techniques to address the primal subproblems inexactly. We demonstrate that PDHCG maintains a linear convergence rate with an improved convergence constant and is also straightforward to implement on GPUs. Extensive numerical experiments affirm that, compared to rAPDHG, our method could significantly reduce the number of iterations required to achieve the desired accuracy and offer a substantial performance improvement in large-scale problems. These findings highlight the significant potential of our proposed PDHCG method to boost both the efficiency and scalability of solving complex QP challenges.

个人简介：

2014年本科毕业于中国科学技术大学少年班学院华罗庚班，18年在香港中文大学系统工程与工程管理系获得博士学位，之后分别在香港中文大学和伦敦帝国理工学院做博后。21年加入上海财经大学任助理教授，24年加入上海交通大学。主要研究兴趣是连续优化及其在机器学习、运营管理以及信号处理中的应用。