154.com皇冠学术报告

Adaptive Iterative Hard Thresholding for Least Absolute 

Deviation Problems with Sparsity Constraints

沈益

（浙江理工大学）

报告时间：2022年11月25日 星期五

报告地点：腾讯会议 166-386-244

报告摘要：

Constrained Least absolute deviation (LAD) problems often arise from sparse regression of statistical prediction and compressed sensing literature.  It is challenging to solve LAD problems with sparsity constraints directly due to non-smoothness of objective functions and non-convex feasible sets. We provide an adaptive iterative hard thresholding method to solve LAD problems with sparsity constraints.  The sequence converges to ground truth linearly under the $l_1$ restricted isometry property condition.  Then we apply our analysis method to the binary iterative hard thresholding (BIHT) algorithm in one-bit compressed sensing. We obtain a tighter error bound compared with our previous work on BIHT.  To some extent, our results can explain the efficiency of BIHT in recovering sparse vectors and make up for the deficiency of the theoretical guarantee of BIHT. Finally, numerical examples demonstrate the validity of our convergence analysis. This is a joint work with Prof. Song Li and Dekai Liu.

报告人简介:

沈益，浙江理工大学数学科学系教授，博导，浙江省应用数学研究会副理事长；毕业于浙江大学数学系，获应用数学博士学位（导师：李松教授）；从事应用调和分析、信息论、逼近论等相关领域的研究；主持国家自然科学基金面上项目、优秀青年科学基金项目、浙江省杰出青年基金项目等省部级项目；在ACHA、IEEE TIT、IEEE TSP、CAGD等期刊发表论文20余篇，曾获“浙江省优秀数学教师”称号。

邀请人： 黄猛