讲座题目：A Newton Interior-Point Method for L0 Factor Analysis
主 讲 人：朱彬 副教授（中山大学）
讲座时间：2025年7月1日（周二）下午14:00-15：30
讲座地点：理学院钱伟长楼 201会议室
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理学院
2025年6月23日
讲座内容简介：
Factor Analysis is an effective way of dimensionality reduction achieved by revealing the low-rank plus sparse structure of the data covariance matrix. The corresponding model identification task is often formulated as an optimization problem with suitable regularizations. In particular, we use the nonconvex discontinuous L0 norm in order to induce the sparsity of the covariance matrix of the idiosyncratic noise. This paper shows that such a challenging optimization problem can be approached via an interior-point method with inner-loop Newton iterations. To this end, we first characterize the solutions to the unconstrained L0 regularized optimization problem through the L0 proximal operator, and demonstrate that local optimality is equivalent to the solution of a stationary-point equation. The latter equation can then be solved using standard Newton's method, and the procedure is integrated into an interior-point algorithm so that inequality constraints of positive semidefiniteness can be handled. Finally, numerical examples validate the effectiveness of our algorithm.
主讲人简介：
Bin Zhu received a B.Eng. degree from Xi'an Jiaotong University, Xi'an, China in 2012 and a M.Eng. degree from Shanghai Jiao Tong University, Shanghai, China in 2015, both in control science and engineering. In 2019, he obtained a Ph.D. degree in information engineering from University of Padova, Padova, Italy, and he had a one-year postdoc position in the same university. Since December 2019, he has been working at the School of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen, China, where he is now an associate professor. His current research interest includes spectral analysis, frequency estimation, and sparsity-promoting techniques for signal processing and machine learning.
Dr. Zhu has been appointed as an Associate Editor of the Editorial Board of the International Conference on System Theory, Control and Computing (ICSTCC) since December 2023. He is a Reviewer (No. 172818) for Mathematical Reviews/MathSciNet, American Mathematical Society. His Erdős number is 4.
