报告题目：A Semismooth Newton-Based Proximal Augmented Lagrangian Method for Joint Estimation of Multiple Gaussian Graphical Models with Clustered Structure
时 间：2026年5月17日（星期日）14：15
地 点：科研楼18号楼1102
主 办：数学与统计学院、分析数学及应用教育部重点实验室、福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）、福建师范大学数学研究中心
参加对象：感兴趣的老师和研究生
报告摘要：Graphs representing complex systems often exhibit shared partial structures across domains while retaining their individual features. This paper focuses on learning multiple Gaussian graphical models with a clustered structure, which promotes similar sparsity patterns and consistent edge values across graphs. To address this problem, we establish a necessary and sufficient condition for the solution to be block diagonal. This property allows the large-scale problem to be decomposed into smaller independent subproblems, significantly reducing computational complexity. We develop an efficient proximal augmented Lagrangian method to solve the problem, where each subproblem is solved by a superlinearly convergent semismooth Newton method. Unlike widely used first-order methods, our approach fully leverages second-order information within the semismooth Newton framework, leading to faster convergence and enhanced robustness. The efficiency and robustness of the proposed algorithm are validated through comparisons with state-of-the-art methods on both synthetic and real-world datasets.
报告人简介：刘勇进，福州大学嘉锡学者特聘教授、博士生导师，福建省闽江教育领军人才闽江特聘教授，担任福州大学数学与统计学院院长、福建省应用数学中心（福州大学）主任。研究兴趣主要包括：最优化理论、方法与应用，大规模数值计算，统计优化等，研究成果在包括Mathematical Programming (Series A)、SIAM Journal on Optimization、SIAM Journal on Scientific Computing等优化与计算领域国际顶级学术期刊上发表。主持国家重点研发计划项目课题1项，主持国家自然科学基金4项，主持教育部、省重点项目等部省级纵向科研项目7项。现任中国数学会理事、中国运筹学会理事、中国运筹学会数学规划分会常务理事、中国运筹学会算法软件与应用分会常务理事、中国统计学会理事、福建省运筹学会会长、福建省数学学会副会长。担任国际期刊Annals of Applied Mathematics编委。