学术报告报告题目: Group Sparse Optimization via L_{p,q} Regularization
报 告 人: 杨晓琪 教授（香港理工大学）
报告时间: 2019年7 月11 日（星期四上午）9:00-10:00
报告地点：4号楼318 室
邀 请 人: 潘少华 教授
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数学学院
2019年7月9日
报告摘要：
In this paper, we investigate a group sparse optimization problem via L_{p;q} 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 L_{p;q} 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 L_{p;q} regularization problems, either by analytically solving some specific L_{p;q} regularization subproblems, or by using the Newton method to solve general L_{p;q} regularization subproblems. In particular, we establish a local linear convergence rate of the proximal gradient method for solving the L_{1;q} regularization problem under some mild conditions and by first proving a second-order growth condition. As a consequence, the local linear convergence rate of proximal gradient method for solving the usual L_q regularization problem (0 < q < 1) is obtained. Finally in the aspect of application, we present some numerical results on both the simulated data and the real data in gene transcriptional regulation.
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。