题目：PADMM for linear inverse problems
报告人：焦雨领（中南财经政法大学统计与数学学院，副教授）
报告地点时间：数学院425报告厅（6月20日上午11点15分）
报告摘要：In this talk, we propose a preconditioned alternating direction method of multipliers (ADMM) to solve linear inverse problems in Hilbert spaces with constraints, where the feature of the sought solution under a linear transformation is captured by a possibly non-smooth convex function. During each iteration step, our method avoids solving large linear systems by choosing a suitable preconditioning operator.In case the data is given exactly, we prove the convergence of our preconditioned ADMM without assuming the existence of a Lagrange multiplier. In case the data is corrupted by noise, we propose a stopping rule using information on noise level and show that our preconditioned ADMM is a regularization method; we also propose a heuristic rule when the information on the noise level is unavailable or unreliable and give its detailed analysis. Numerical examples are presented to test the performance of the proposed method.
报告人简介: 焦雨领，2014年毕业于武汉大学数学与统计学院, 现就职于中南财经政法大学统计与数学学院统计学系，文澜学者。主要从事统计计算，高维统计推断，机器学习，反问题，图像处理，数据科学中的建模和随机、并行、分布式算法的研究。主持国家自然科学基金青年项目和湖北省自然科学基金面上项目各一项，中央高校研究项目3项。在包括 SIAM Journal on Numerical Analysis, Applied and Computational Harmonic Analysis, Inverse Problems, IEEE Transactions on Signal Processing, IEEE Transactions on Geoscience and Remote Sensing, Journal of Scientific Computing, Advanced in Computational Mathematics 等在内的国际一类、二类期刊上发表20余篇SCI论文并制作了10个MATLAB软件包。
