报告题目：Some Recent Advances in Polynomial Optimization
报告人：Guoyin Li 副教授（The University of New South Wales）
报告校内联系人：张立卫 教授 联系电话：84708351-8097
报告摘要: Optimization problems involving polynomial functions are of great importance in applied mathematics and engineering, and they are intrinsically hard problems. They arise in important engineering applications such as the sensor network localization problem, and provide a rich and fruitful interaction between algebraic-geometric concepts and modern convex programming. The talk will be divided into two parts. In the first part, I will describe the key results in this exciting area, highlighting the geometric and conceptual aspects as well as recent work on exact semi-definite program relaxation for polynomial optimization problems. In the second part, I will explain how the semi-algebraic structure helps us to analyse the explicit convergence rate of some important and powerful algorithms such as alternating projection algorithm, proximal point algorithm and Douglas-Rachford algorithm. Applications to tensor computations and sparse optimization problems will be discussed (if time is permitted).
报告人简介：Guoyin Li received his Ph.D. on December 2007 from The Chinese University of Hong Kong. His research interest spans from optimization, variational analysis and multilinear algebra. After 3 years of postdoctoral training at The University of New South Wales (UNSW Sydney), Australia, he joined UNSW as a lecturer in 2011 where he is currently a Reader/Associate Professor in the school of mathematics and statistics. He has published over 80 journal articles in top quality journals including Foundation of Computational Mathematics, SIAM Journal on Optimization, Mathematical Programming, Numerische Mathematik, Mathematics of Computations, and Journal of Functional Analysis. He received a midcareer Future Fellowship from Australian Research Council during 2014-2018, and an inviting visiting fellowship from the Issac Newton Institute at Cambridge University in August 2013. He was also awarded the 2019 International Consortium of Chinese Mathematicians (ICCM) Best Paper Award, 2019 Journal of Global Optimization Best Paper Award, an international collaboration award from Australian Research Council in 2011, and the 2015 OPTL best paper award by the Springer journal “Optimization Letters”.