报告题目：Proximal methods for nonsmooth and nonconvex fractional programs: when sparse optimization meets fractional programs

报告人： Guoyin Li

报告时间：9月16日 15：30 -16：30

报告地点：腾讯会议：353-708-298

报告摘要：Nonsmooth and nonconvex fractional programs are ubiquitous and also highly challenging. It includes the composite optimization problems studied extensively lately, and encompasses many important modern optimization problems arising from diverse areas such as the recent proposed scale invariant sparse signal reconstruction problem in signal processing, the robust Sharpe ratio optimization problems in finance and the sparse generalized eigenvalue problem in discrimination analysis. In this talk, we will introduce extrapolated proximal methods for solving nonsmooth and nonconvex fractional programs and analyse their convergence behaviour. Interestingly, we will show that the proposed algorithm exhibits linear convergence for sparse generalized eigenvalue problem with either cardinality regularization or sparsity constraints. This is achieved by identifying the explicit desingularization function of the Kurdyka-Lojasiewicz inequality for the merit function of the fractional optimization models. Finally, if time permits, we will present some preliminary encouraging numerical results for the proposed methods for sparse signal reconstruction and sparse Fisher discriminant analysis.

报告人简介：Guoyin Li received his Ph.D. in 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 professor and research director in the school of mathematics and statistics. He has published over 90 journal articles in top quality journals including Foundation of Computational Mathematics, SIAM Journal on Optimization, Mathematical Programming, Mathematics of Operations Research, 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, the 2015 OPTL best paper award by the Springer journal “Optimization Letters” and an International Collaboration Award from Australian Research Council in 2011. He is currently on the editorial board of "Journal of Optimization Theory and its Applications", "Mathematical Methods of Operation Research" and "Optimization Letters".