主讲人：胡耀华

主办单位：数学与大数据学院

讲座时间：2023年3月29日 16：00——17:00

讲座地点：知津楼C303

内容简介：

Sparse optimization is a popular research topic in applied mathematics and optimization, and nonconvex sparse regularization problems have been extensively studied to ameliorate the statistical bias and enjoy robust sparsity promotion capability in vast applications. However, puzzled by the nonconvex and nonsmooth structure in nonconvex regularization problems, the convergence theory of their optimization algorithms is still far from completion: only the convergence to a stationary point was established in the literature, while there is still no theoretical evidence to guarantee the convergence to a global minimum or a true sparse solution.

   This talk aims to find an approximate global solution or true sparse solution of an under-determined linear system. For this purpose, we propose two types of iterative thresholding algorithms with the continuation technique and the truncation technique respectively. We introduce a notion of limited shrinkage thresholding operator and apply it, together with the restricted isometry property, to show that the proposed algorithms converge to an approximate global solution or true sparse solution within a tolerance relevant to the noise level and the limited shrinkage magnitude. Applying the obtained results to nonconvex regularization problems with SCAD, MCP and Lp penalty and utilizing the recovery bound theory, we establish the convergence of their proximal gradient algorithms to an approximate global solution of nonconvex regularization problems.

主讲人简介：

胡耀华，深圳大学数学与统计学院教授，国家优秀青年基金获得者，博士生导师，香港理工大学兼职博士生导师，兼任中国运筹学会数学规划分会青年理事。主要从事连续优化理论、算法与应用研究，先后主持国家自然科学基金项目4项，省市级科研项目10余项。在SIAM Journal on Optimization, Journal of Machine Learning Research, European Journal of Operational Research, Briefings in Bioinformatics等国际期刊发表论文40余篇，申请3项国家发明专利，开发多个生物信息学工具包与网页服务器。