应304am永利集团官网李朋副教授邀请, 中山大学数据科学与计算 机学院李洽副教授, 将于2022年11月3号(星期四)上午10:00在线举办学术报告.

报告题目：First-orderAlgorithms forAClass ofFractionalOptimizationProblems

腾讯会议ID:609-555-634

报告摘要:We consider in this paper a class of single-ratio fractional minimization problems, in which the numerator of the objective is the sum of a nonsmooth nonconvex function and a smooth nonconvex function while the denominator is a nonsmooth convex function. In this work, we first derive its first-order necessary optimality condition, by using the first-order operators of the three functions involved. Then we develop first-order algorithms, namely, the proximity-gradient-subgradient algorithm (PGSA),PGSA with monotone line search (PGSA-ML) and PGSA with nonmonotone line search (PGSA-NL). It is shown that any accumulation point of the sequence generated by them is a critical point of the problem under mild assumptions. Moreover, we establish global convergence of the sequence generated by PGSA or PGSA-ML and analyze its convergence rate, by further assuming the local Lipschitz continuity of the nonsmooth function in the numerator, the smoothness of the denominator and the Kurdyka-Lojasiewicz (KL) property of the objective. The proposed algorithms are applied to the sparse generalized eigenvalue problem associated with a pair of symmetric positive semidefinite matrices and the corresponding convergence results are obtained according to their general convergence theorems. We perform some preliminary numerical experiments to demonstrate the efficiency of the proposed algorithms.

报告人简介

李洽, 中山大学数据科学与计算机学院副教授、博士生导师. 2013年获中山大学数学(信息计算科学方向)博士学位；博士期间曾赴美国Syracuse University数学系访问一年；现任中山大学计算机学院科学计算系副主任, 广东省计算数学学会理事. 研究领域包括最优化理论、算法及在机器学习、数据分析与图像处理等领域的应用, 相关论文在ACHA、SIOPT、IP、TMI等应用与计算数学知名期刊上发表, 其中一篇获评Inverse Problems期刊2017年度Highlights. 主持项目包括国家自然科学基金两项(青年基金与面上项目)以及广东省自然科学基金, 参与项目包括国家重大研究计划集成项目、广东省重点研发计划.详情请见李洽教授个人主页：https://cse.sysu.edu.cn/content/2566

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2022年10月28日