报告题目:Augmented Lagrangian method for linear inverse problems with multiple repeated measurement data
摘要:We consider determining R-minimizing solutions of linear ill-posed problems A x = y, where R is a proper convex penalty function. Assuming that multiple repeated independent identically distributed unbiased data of y are available, we consider the augmented Lagrangian method to reconstruct the R-minimizing solution using the average of these data. By terminating the method by either an {\it a priori} stopping rule or a variant of the discrepancy principle, we provide the convergence analysis and derive convergence rates when the sought solution satisfies certain variational source conditions. Various numerical results are reported to test the performance of the method.
报告人简介:王薇,理学博士,教授,硕士生导师。2011年4月在必赢获得理学博士学位。2011年7月至2013年7月在复旦大学从事博士后研究工作。研究方向为反问题理论与计算,也包括地震波全波形反演、EIT问题、CT不完全数据的图像重构等应用。主持国家自然科学基金项目2项(青年基金项目、面上项目),浙江省自然科学基金项目2项(青年基金、一般项目),在Numer Math、Inverse Problems等有影响力的国际学术期刊上发表SCI论文30余篇。
报告地点:理学楼401
报告时间:2023.08.08 14:00-17:00