题  目：Bregman ADMM for Robust Fused Lasso Estimation with Doubly Nonconvex Regularizers 

报告人：靳正芬 副教授

单  位：河南科技大学

时  间：2023年10月11日 10:30

地  点：河南大学龙子湖校区九章学堂C座301

摘要：The fused Lasso has been playing an important role in variable selection and dimensionality reduction for high dimensional linear regression, because it can effectively deal with the case where two adjacent variables exhibit strong correlation with each other and gain sparse solutions under the Gaussian noise. However, it has poor robustness for the case with non-Guassian noise with heavy-tailed distribution. Moreover, instead of a convex relaxation with the l1-norm, a proper nonconvex regularization can achieve a sparse estimation with fewer measurements, and is more robust against noisy cases. In this paper, we propose a robust fused Lasso with doubly nonconvex regularizers replacing the l1-norm terms and present a Bregman ADMM for solving it. By using the Kurdyka-Lojasiewicz property exhibited in the underlining problems, we give the convergence analysis of the proposed Bregman ADMM. Extensive Simulation and real numerical experiments are presented to demonstrate the  robustness of the proposed model and the high efficiency of the proposed algorithm.

报告人简介：靳正芬，河南科技大学，副教授。2021年5月至今，在北京航空航天大学数学科学学院从事博士后研究工作。研究方向是最优化理论、方法及其应用、大规模稀疏与低秩优化、统计优化。主持1项国家自然科学基金青年项目和1项河南省自然科学基金青年项目，参与5项国家自然科学基金项目。在Numerical Linear Algebra with Applications, Journal of Scientific Computing和Applied Mathematical Modelling等国外著名期刊上发表论文10余篇。现为中国运筹学会数学规划分会青年理事，中国运筹学会宣传工作委员会委员，河南省运筹学会组织工作委员会委员。