發布單位：成果專利綜合科 [2019-07-05 17:07:49] 打印此信息
題目一：Algorithmic Development for Computing B-stationary Points of a Class of Nonsmooth DC Programs
內容簡介：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 augmentedLagrangian methods for solving them and show that they converge to a B-stationary point under much weaker assumptions than those imposed in the literature.
報告人：加拿大西蒙弗雷澤大學(Simon Fraser University)呂召松(LUZHAOSONG)教授
報告人簡介：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. ArkadiNemirovski. 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.
題目二：Interpolation and Expansion on Orthogonal Polynomials
內容簡介：The convergence rates on polynomial interpolation in most cases are estimatedby Lebesgue constants. These estimates may be overestimated for some specialpoints 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.
報告人簡介：二級教授、博士生導師、湖南省計算數學與應用軟件學會理事長，主要從事高頻振蕩問題、正交多項式理論等研究，在SIAM J. Numer.Anal.、SIAM J. Sci. Comput.、SIAM J. Optimization、Math.Program.、Numer.Math.、Math.Comput.等國際計算數學頂級期刊發表系列論文，Wang-Xiang給出的有關高斯-勒讓德多項式零點與積分權的重心插值公式被國際權威Trefethen稱爲多項式關鍵十一個公式之一，高頻振蕩問題的研究也成爲國際上幾個重要團隊之一；2006年入選教育部新世紀優秀人才計劃，2009年入選Who is Who in the World，2011年入選湖南省学科带头人培养对象；2003年9月-2004年9月在英國劍橋大學訪問，2004年11月-2005年9月獲日本JSPS資助任弘前大學長期特邀研究員，2008年9月-2009年9月香港理工大學研究員。
題目三：Towards effective spectral and hp methods for PDEs with integral fractional Laplacian in multiple dimensions
內容簡介：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.
報告人簡介：博士生導師。主要研究領域爲譜方法求解偏微分方程，電磁學中的高性能計算方法等。在SIAM J. Numer. Anal., SIAM J. Appl. Math., SIAM J. Sci. Comput.,Math. Comp.等國際知名計算數學期刊上發表論文七十余篇，並且由Springer出版合著《SPECTRAL METHODS: Algorithms, Analysis and Applications》。