报告题目：Robust Principal Component Analysis with Rank and Cardinality Regularization under Matrix Factorization

报 告 人：边伟 教授（哈尔滨工业大学）

报告时间：2026年4月27日（星期一）8:00—8:40

报告地点：6776永利集团114（小报告厅）      

校内联系人：张立卫 教授         联系方式：84708351-8320

报告摘要：Robust principal component analysis (RPCA) is an important representative method in data analysis. It is usually viewed as an optimization problem involving the rank and $\ell_0$-norm of matrices. In this paper, we study the rank and $\ell_0$ regularized matrix optimization problem based on matrix factorization for the first time. In the context of RPCA, the low-rank structure provides computational benefits for the factorized model. For the rank and $\ell_0$ regularized model and its factorization model, we establish their equivalences on global minimizers and stationary points, respectively. Furthermore, we construct a broadly applicable equivalent nonconvex relaxation framework for the constrained factorization model, and establish the equivalence between it and its diverse relaxations in the sense of global minimizers and stationary points with strong optimality conditions (called strong stationary points). For the general factorization problem with lower semicontinuous regularizers and a loss function whose gradient is locally Lipschitz, we propose a novel proximal gradient-based algorithm based on joint and alternating calculation with convergence to its limiting- critical points. We prove that the proposed algorithm can attain the stationary points of the rank and $\ell_0$ regularized problem and its adaptive counterpart can attain the strong stationary points of the constrained factorization problem and its relaxation problems, respectively.

报告人简介：边伟，哈尔滨工业大学数学学院，教授、博士生导师。2004年和2009年于哈尔滨工业大学分别获得学士和博士学位。2010-2012年访问香港理工大学，跟随陈小君教授从事博士后工作。主要研究领域为：最优化理论与算法。先后在 Math. Program., Math. Oper. Res., SIAM J. Optim., SIAM J. Numer. Anal., SIAM J. Sci. Comput., SIAM J. Imaging Sci. 等期刊发表多篇学术论文。现任SCI期刊Journal of Optimization Theory and Application编委，中国运筹学会常务理事，黑龙江省数学会常务理事。