报告题目：An Accelerated Alternating Partial Bregman Algorithm for ReLU-based Matrix Decomposition

报告时间：2024年12月14日 16：00

报告地点：龙洞校区行政楼610

报 告 人：韩德仁教授（北京航空航天大学）

主 持 人：常静雅

报告摘要：We focus on exploiting the inherited low-rank structure of a non-negative and sparse matrix based on the rectified linear unit(ReLU) activation function. We explore the ReLU-based regularized matrix decomposition model and introduce an accelerated alternating partial Bregman proximal gradient method (AAPB) for solving it. Under mild assumptions, we demonstrate the sublinear convergence and global convergence of the proposed algorithm and provide closed-form solutions for several regularizations by carefully choosing the kernel generating distance. The advantage of our algorithm is that the smooth adaptable constant only needs to be computed once, and some variables can be updated in parallel.Numerical experiments on synthetic and real datasets confirm the effectiveness of our model and algorithm.

报告人简介：韩德仁，教授，博士生导师，北京航空航天大学数学科学学院院长、教育部数学类专业教指委秘书长。从事大规模优化、变分不等式问题及其应用研究工作，发表多篇学术论文。曾获中国运筹学会青年科技奖，江苏省科学技术奖等奖项;主持国家自然科学基金重点项目、杰出青年基金项目等多项项目。担任中国运筹学会副理事长；《数值计算与计算机应用》、《Journal of the Operations Research Society of China》、《Journal of Global Optimization》、《Asia-Pacific Journal of Operational Research》编委。