Shenzhen University School of Mathematical Sciences  

Liyuan Scholars Colloquium No. 134  

Lecture Title: Alternating Minimization for Square Root Principal Component Pursuit  

Speaker: Professor Li Xudong (Fudan University)  

Lecture Time: 4:30–5:30 PM, June 17, 2025  

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

Abstract: Recently, the square root principal component pursuit (SRPCP) model has garnered significant research interest. Literature shows that the SRPCP model ensures robust matrix recovery with a universal, constant penalty parameter. While its statistical advantages are well-documented, computational aspects from an optimization perspective remain largely unexplored. This talk focuses on developing efficient optimization algorithms for the SRPCP problem. Specifically, we propose a tuning-free alternating minimization (AltMin) algorithm, where each iteration involves subproblems with closed-form optimal solutions. We also introduce techniques based on the variational formulation of the nuclear norm and Burer-Monteiro decomposition to accelerate the AltMin method. Extensive numerical experiments validate the efficiency and robustness of our algorithms.  

Biography of the Speaker: Li Xudong is a professor at the School of Data Science, Fudan University, and a Distinguished Professor of the Ministry of Education. His research has been published in top international journals on operations research and artificial intelligence conferences. He has received the Young Scholar Award of the International Society for Mathematical Optimization (2019, awarded once every three years), Outstanding Paper Award at ICML 2022, and the Young Scientist Award of the Chinese Operations Research Society (2022). He currently serves on the editorial boards of Mathematical Programming and Mathematical Programming Computation.  

All faculty and students are welcome to attend!  

School of Mathematical Sciences  

June 16, 2025