Alternating minimization for square root principal component pursuit and beyond

报告摘要：Square-root principal component pursuit (SRPCP) offers robust matrix recovery guarantees with a universal, constant penalty parameter. In this talk, we present a tuning-free alternating minimization algorithm whose subproblems admit closed-form solutions. We further improve its efficiency using the variational formulation of the nuclear norm and low-rank factorization. Numerical experiments demonstrate the efficiency and robustness of the proposed methods. Motivated by the underlying spectral subproblems, we also establish exact low-dimensional reformulations for a broader class of regularized spectral approximation problems, including weighted variants under suitable structural conditions.

报告人简介：郦旭东，复旦大学大数据学院、数学科学学院、应用数学中心特聘教授，研究成果发表于运筹优化国际权威期刊与人工智能顶级会议。目前担任期刊 Mathematical Programming 及 Mathematical Programming Computation 编委。