题目一：Algorithmic Development for Computing B-stationary Points of a Class of Nonsmooth DC Programs
内容简介：In the first part of this talk, we study a convex-constrained nonsmooth DC program in which the concave summand of the objective is an infimum of possibly infinitely many smooth concave functions. We propose some algorithms by using nonmonotone linear search and extrapolation techniques for possible acceleration for this problem, and analyze their global convergence, sequence convergence and also iteration complexity. We also propose randomized counterparts for them and discuss their convergence.In the second part we consider a class of DC constrained nonsmooth DC programs. We propose penalty and augmented Lagrangian methods for solving them and show that they converge to a B-stationary point under much weaker assumptions than those imposed in the literature.
报告人：加拿大西蒙弗雷泽大学(Simon Fraser University) 吕召松(LUZHAOSONG) 教授
报告人简介：Dr. Zhaosong Lu is a full Professor of Mathematics and an associate faculty member in Statistics and Actuarial Science at Simon Fraser University. He received PhD in Operations Research from the School of Industrial and Systems Engineering of Georgia Tech in 2005 under the supervision of Dr. Renato Monteiro and Dr. Arkadi Nemirovski. He was a Visiting Assistant Professor of Mathematical Sciences at Carnegie Mellon University during 2005-2006. He was also a Visiting Associate Professor at Texas A&M University and Arizona State University, and a Visiting Researcher at Microsoft Research, Redmond during 2012-2013. His research interests include theory and algorithms for continuous optimization, and applications in data analytics, finance, statistics, machine learning, image processing, engineering design, and decision-making under uncertainty. He was a finalist of INFORMS George Nicholson Prize. He has published numerous papers in major journals of his research areas such as: SIAM Journal on Optimization, SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, SIAM Journal on Matrix Analysis and Application, Mathematical Programming, and Mathematics of Operations Research. He also served on INFORMS George Nicholson Prize Committee in 2014 and 2015. Currently, he is an Associate Editor for SIAM Journal on Optimization, Computational Optimization and Applications, and Big Data and Information Analytics.
题目二：Interpolation and Expansion on Orthogonal Polynomials
内容简介：The convergence rates on polynomial interpolation in most cases are estimated by Lebesgue constants. These estimates may be overestimated for some special points of sets for functions of limited regularities. In this talk, new formulas on the convergence rates are considered. Moreover, new and optimal asymptotics on the coefficients of functions of limited regularity expanded in forms of Jacobi and Gegenbauer polynomial series are presented. All of these asymptotic analysis are optimal. Numerical examples illustrate the perfect coincidence with the estimates.
报告人：中南大学 向淑晃 教授
报告人简介：二级教授、博士生导师、湖南省计算数学与应用软件学会理事长，主要从事高频振荡问题、正交多项式理论等研究，在SIAM J. Numer. Anal.、SIAM J. Sci. Comput.、SIAM J. Optimization、Math. Program.、Numer. Math.、Math. Comput.等国际计算数学顶级期刊发表系列论文，Wang-Xiang给出的有关高斯-勒让德多项式零点与积分权的重心插值公式被国际权威Trefethen称为多项式关键十一个公式之一，高频振荡问题的研究也成为国际上几个重要团队之一；2006年入选教育部新世纪优秀人才计划，2009年入选Who is Who in the World，2011年入选湖南省学科带头人培养对象；2003年9月-2004年9月在英国剑桥大学访问，2004年11月-2005年9月获日本JSPS资助任弘前大学长期特邀研究员，2008年9月-2009年9月香港理工大学研究员。
题目三：Towards effective spectral and hp methods for PDEs with integral fractional Laplacian in multiple dimensions
内容简介：PDE with integral fractional Laplacian is a powerful tool in modelling anomalous diffusion and nonlocal interactions, but its numerical solution can be very difficult especially in multiple dimensions. In fact, many of such nonlocal models are more physically motivated and naturally set in unbounded domains. In this talk, we shall present a superfast spectral-Galerkin method with two critical components (i) based on the Dunford-Taylor formulation of fractional Laplacian operator, and (ii) using Fourier-like mapped Chebyshev functions as basis. We shall also report some of our recent attempts for integral fractional Laplacian in bounded domains, which are deemed even more notoriously difficult in effective numerical discretisations. Along this line, we work with the formulation associated with the Fouririer transformations, and derive a number of useful analytical formulas which are essential for the algorithm development.
报告人：新加坡南洋理工大学 王立联 教授
报告人简介：博士生导师。主要研究领域为谱方法求解偏微分方程，电磁学中的高性能计算方法等。在SIAM J. Numer. Anal., SIAM J. Appl. Math., SIAM J. Sci. Comput.,Math. Comp.等国际知名计算数学期刊上发表论文七十余篇，并且由Springer出版合著《SPECTRAL METHODS: Algorithms, Analysis and Applications》。
时 间：2019年7月9日（周二）下午3：00始
地 点：南海楼224室
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信息科学技术学院
2019年7月5日