上海管理论坛第559期

题目：求解大规模结构线性系统的分裂交替算法

演讲人：赵云彬教授，广东省智能工业孪生与优化工程技术研究中心主任

主持人：林贵华教授，上海大学管理学院

时间：2025年11月12日（周三），上午8:15

地点：上海大学校本部东区1号楼管理学院420会议室

主办单位：上海大学管理学院、上海大学管理学院青年教师联谊会

演讲人简介：

赵云彬，知名优化专家，广东省智能工业孪生与优化工程技术研究中心主任，深圳市大数据研究院教授，深圳国际工业与应用数学中心教授，香港中文大学（深圳）数据科学学院兼职教授。2001-2008年任职于中国科学院，2007-2020年任职于英国伯明翰大学。长期从事运筹与优化、信号处理、压缩感知等领域研究，在SIAM J Optim、SIAM J Contr Optim、SIAM J Matrix Anal Appl、Math Oper Res等著名期刊发表论文80余篇，出版英文专著1部，担任Appl Math Compu等多个期刊编委。

演讲内容简介：

A class of splitting alternating algorithms is proposed for finding the sparse solution of linear systems with concatenated orthogonal matrices. Depending on the number of matrices concatenated, the proposed algorithms are classified into the two-block splitting alternating algorithm and the multi-block splitting alternating algorithm. These algorithms aim to decompose a large-scale linear system into two or more coupled subsystems, each significantly smaller than the original system, and then combine the solutions of these subsystems to produce the sparse solution of the original system. The proposed algorithms only involve matrix-vector products and reduced orthogonal projections. It turns out that the proposed algorithms are globally convergent to the sparse solution of a linear system if the matrix (along with the sparsity level of the solution) satisfies a coherence-type condition. Numerical experiments indicate that the proposed algorithms are very promising and can quickly and accurately locate the sparse solution of a linear system with significantly fewer iterations than several mainstream iterative methods.

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