金其年教授学术讲座
通讯员:  发布人:刘巍  发布时间:2017-06-22   浏览次数:550

报告人:金其年(National University of Australia

报告时间628号下午3:00400

报告地点:文波楼4楼会议室

题目Regularization of inverse problems by the augmented Lagrangian method

摘要The augmented Lagrangian method was developed by Hestenes and Powell in 1969 independently. Since then this method has become popular for solving well-posed constrained optimization problems. In this talk we will consider the application of the augmented Lagrangian method for linear ill-posed inverse problems. Due to the ill-posedness of the problems this method shows semi-convergence during the iteration. We will discuss how to terminate the iteration in order to produce a satisfactory approximate solution. We first discuss the discrepancy principle which relies on the accurate information on the noise level. We then consider a heuristic stopping rule of Hanke-Raus type which does not use any information on noise level and is totally data driven. We will provide a posteriori error estimates and convergence results for this heuristic rule.

  

报告人简介:金其年教授, 国际著名反问题专家。 1997年于复旦大学数学系获得博士学位, 然后进入南京大学数学系从事科研和教学工作,并于2000年晋升为副教授。后赴美国留学, 在Rutgers大学从事偏微分方程和几何分析的研究,并于2006年获得数学博士学位。之后分别在德州大学Austin分校和Virginia Tech从事博士后和访问学者工作。2011年加入澳大利亚国立大学。2017年获得澳大利亚基金委的Future Fellowship (相当于中国的国家杰出青年基金)。 从事反问题,数值分析, 偏微分方程, 几何分析方面的研究。 在包括SIAM J.Numer. Anal., Inverse Problems, Numer. Math, Math.Comput. SIAM J. Uncertainty Quantification等在内的国际顶级期刊发表论文40多篇。