报告题目：Projected Subgradient Method under Sparsity Constraint…

报 告 人：李松

时 间：2021年9月23日（周四）下午14:30-15:30

地 点：腾讯会议会议号642745482

简 介：In this talk, a projected subgradient method under sparsity constraints is proposed to solve the general convex model and some convergence results are established. A stronger convergence theorem for strongly convex functions without assumption on differentiable condition is also established. Furthermore, the corresponding stochastic projected subgradient method is provided with convergence guarantee. In our settings, BIHT is a special case of the projected subgradient method. Therefore, the convergence analysis can be applied to BIHT naturally. Then, we apply the projected subgradient method to some related non-convex optimization models arising in compressive sensing with 1-constraint, sparse support vector machines, and rectifier linear units regression. Finally, some numerical examples are presented to show the validity of our convergence analysis. The numerical experiments also show that the proposed projected subgradient method is very simple to implement, robust to sparse nois...

报告题目：数苑博雅讲座：Polynomial mean complexity and Sarnak co…

报 告 人：黄文

时 间：2021年9月20日（周一）下午4:50-5:50

地 点：6号楼二楼报告厅

简 介：We will review some recent progresses in Sarnak conjecture related to complexity. In particular, we will investigate the relation between {0,1}- sequences with polynomial mean complexity and the Logarithmic Sarnak conjecture.

报告题目：数苑博雅讲座：The measure and fractal properties of Di…

报 告 人：吴军

时 间：2021年9月20日(周一)下午3:40-4:40

地 点：6号楼二楼报告厅

简 介：Dirichlet’s theorem is a fundamental result in metric Diophantine approxima- tion. The improvability of this theorem was first considered by Davenport and Schmidt. After them, Kleinbock and Wadleigh proposed the concept of Dirich- let improvable point formally in 2018 and launched relevant work. Their results show that the improvability of Dirichlet’s theorem is concerned with the growth of the product of the partial quotients. In this talk, we present some results on the size of uniformly Dirichlet non– improvable set, the size of exact Dirichlet non–improvable set and metric prop- erties of the product of the partial quotients in continued fractions.