报告承办单位: 数学与统计学院

报告题目: Sparse nonlinear SDP: stationarity and algorithm

报告人姓名: 罗自炎

报告人所在单位: 北京交通大学

报告人职称: 教授、博士生导师

报告时间: 2026年6月28日 星期日 下午17:30

报告地点: 理科楼A212

邀请人：李姣

报告摘要: The sparse nonlinear semidefinite programming (SNSDP) problem aims to minimize a smooth objective function subject to nonlinear positive semidefinite cone constraint and additional sparse constraint. This class of optimization problem is generally nonconvex, discontinuous, and computationally NP-hard. By virtue of projection operators onto the positive semidefinite matrix cone and the sparse set, we derive the optimality conditions for SNSDP based on the newly introduced strong Lagrangian stationary points. According to the reformulated Lagrangian equation system, an efficient Lagrange semi-smooth Newton-type algorithm with correction steps (LSNC) is proposed. Furthermore, the local quadratic convergence of the developed method is established under relatively weak regularity assumptions, including the restricted constraint nondegeneracy (RCN) and the restricted weak second-order condition (RW-SOC). Preliminary numerical experiments verify the computational efficiency of the proposed LSNC method. This is a joint work with Hongjie Lin and Shenglong Zhou.

报告人简介：罗自炎，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、算法软件与应用分会理事、CSIAM优化及其应用专委会委员、中国高等教育学会教育数学专业委员会资深理事。主要从事大规模张量优化、稀疏优化、统计学习方法及其在智慧交通、互联网流量异常检测、压缩感知、图像处理与视频分析等方面的应用研究，学术成果发表在Nature Machine Intelligence、SIOPT、MP、MOR、IEEE TSP、IEEE TWC、JMLR等重要期刊，合著SIAM出版社英文专著1部，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、2023年入选国家级青年人才计划。