报告题目：Normal Cones Intersection Rule and Optimality Analysis for Low-Rank Matrix Optimization with Affine Manifolds

报告人：罗自炎 教授（北京交通大学 数学与统计学院）

报告时间：2023年6月16日（星期五） 15:00-16:00

报告地点：海山楼（创新园大厦）A0331

校内联系人：宋晓良 副教授

报告摘要：The low-rank matrix optimization with affine manifolds (rank-MOA) aims to minimize a continuously differentiable function over a low-rank set intersecting with an affine manifold. In this talk, we will give the optimality analysis for rank-MOA. As a cornerstone, the intersection rule of the Fréchet normal cone to the feasible set of rank-MOA is established under some mild linear independence assumptions. Aided with the resulting explicit formulae of the underlying normal cones, the so-called F-stationary point and the α-stationary point of rank-MOA are investigated and the relationship with local/global minimizers are then revealed in terms of first-order optimality conditions. Furthermore, the second-order optimality analysis, including the necessary and the sufficient conditions, is proposed based on the second-order differentiation information of the model. All these results will enrich the theory of low-rank matrix optimization and give potential clues to designing efficient numerical algorithms for seeking low rank solutions. Meanwhile, two specific applications of rank-MOA are discussed to illustrate our proposed optimality analysis.

报告人简介：罗自炎，女，北京交通大学数学与统计学院教授、博士生导师，中国运筹学会数学规划分会副秘书长，中国运筹学会女性工作委员会委员。曾为美国斯坦福大学、新加坡国立大学、英国南安普顿大学访问学者，香港理工大学研究助理等。发表SCI论文40余篇(ESI高被引论文2篇)，涉及《Math Program》《SIAM J Optim》《J Mach Learn Res》《IEEE Trans Signal Process》《SIAM J Matrix Anal Appl》等国际权威期刊。合作撰写美国SIAM出版社英文专著1部、中文著作1部；主持国家自然科学基金“面上”、“青年”项目、北京市自然科学基金“重点”项目，参与国家自然科学基金“重点”项目，国家重点研发计划等。获教育部自然科学奖二等奖、中国运筹学会青年科技奖提名奖、北京市青年教师教学基本功比赛二等奖、北京市本科毕设论文优秀指导教师等。主要研究兴趣：大规模稀疏低秩优化、张量优化、机器学习，及其在压缩感知、视频分析、智慧交通中的应用。