报告题目：Group Sparse Optimization via Lower Order Regularization

报告人：杨晓琪 香港理工大学应用数学系教授、博士生导师

报告时间：2020年1月5日（周日） 下午15：30

报告地点：数学与统计学院会议室

主持人：方东辉 教授

报告人简介：杨晓琪，1994年博士毕业于澳大利亚新南威尔士大学应用数学系。现任香港理工大学应用数学系教授，博士生导师。主要从事非线性最优化的研究及其在金融问题中的应用，已经在 Management Science，Operations Research，Mathematics of Operations Research，SIAM Journal on Optimization 等国际刊物发表 200 多篇学术论文，撰写了3本专著。先后主持香港政府基金项目 16 项，2000 年获美国 ISI 经典引用奖（ISI Citation Classic Award），2001 ，2018年获香港理工大学校长杰出贡献奖，2006 年获得重庆市自然科学一等奖。2008年及2014年分别与重庆师范大学合作成功申请到国家重点项目。

摘  要：In this paper, we investigate a group sparse optimization problem via lower order regularization in three aspects: theory, algorithm and application. In the theoretical aspect, by introducing a notion of group restricted eigenvalue condition, we establish an oracle property and a global recovery bound for any point in a level set of the regularization problem, and by virtue of modern variational analysis techniques, we also provide a local analysis of recovery bound for a path of local minima. In the algorithmic aspect, we apply the well-known proximal gradient method to solve the lower order regularization problems, either by analytically solving some specified lower order regularization subproblems, or by using the Newton method to solve general lower order regularization subproblems. In particular, we establish a local linear convergence rate of the proximal gradient method for solving the regularization problem under some mild conditions and by first proving a second-order growth condition. Finally in the aspect of application, we present some numerical results on both the simulated data and the real data in gene transcriptional regulation.