报告时间：2023年7月20日（星期四）15:00-16:00

报告地点：翡翠科教楼B楼1710

报告人：曾超副教授

工作单位：南开大学

举办单位：数学学院

报告简介：

Schatten p-quasi-norm minimization has advantages over nuclear norm minimization in recovering low-rank matrices. However, Schatten p-quasi-norm minimization is much more difficult, especially for generic linear matrix equations. We first extend the lower bound theory of l_p minimization to Schatten p-quasi-normminimization. Motivated by this property, we propose a proximal linearization method, whose subproblems can be solved efficiently by the (linearized) alternating direction method of multipliers. The convergence analysis of the proposed method involves the nonsmooth analysis of singular value functions.We give a necessary and sufficient condition for a singular value function to be a Kurdyka–Lojasiewicz function. The subdifferentials of related singular value functions are computed. The global convergence of the proposed method is established under some assumptions. Experiments on matrix completion, Sylvester equation and image deblurring show the effectiveness of the algorithm.

报告人简介：

曾超，南开大学副教授。本科和博士毕业于中科大，之后在南开大学、香港浸会大学、香港大学等学校做博士后研究。研究方向为数值代数、数值优化、图像处理。在Numer. Math.，SIAM J. Numer. Anal., SIAM J. Matrix Anal. Appl. , SIAM J. Imaging Sci.等期刊发表论文十余篇。