报告题目：Proximal Methods for Nonsmooth and Nonconvex Fractional Programs: When Sparse Optimization Meets Fractional Programs

主 讲 人：李国胤教授

单 位：新南威尔士大学澳大利亚

时 间：12月15日15:00

腾 讯 ID：670-613-202

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.

简 介：

李国胤，教授，在吴恭孚(Kung Fu Ng)教授的指导下，于2007年在香港中文大学获得博士学位，之后到新南威尔士大学做博士后，在V. Jeyakumar教授的指导下成为研究员。获得过澳大利亚研究理事会(ARC)的国际合作奖；澳大利亚研究理事会(ARC)的Future Fellowship(2014-2017)；澳大利亚研究理事会(ARC)的博士后奖学金(2010-2013)；澳大利亚研究理事会的发现奖助金（2010-2013）；澳大利亚研究理事会的发现奖助金(2012-2014)。2021年，晋升为教授。主要从事不确定性优化、数值优化、半定规划、非光滑分析和变分分析、凸分析和泛函分析、全局优化和张量分析等。在Mathematical Programming、SIAM Journal on Optimization等杂志上发表高水平学术论文80余篇。主持多项澳大利亚自然科学基金以及香港科研基金等，先后受邀到英国、法国、美国等多个国家进行访学和学术报告。