关于举行李洽副教授（中山大学）学术报告的通知

报告题目: First-order algorithms for fractional optimization problems 

报 告人: 李洽 副教授

报告时间: 2023年3月12日（星期日）14:50-15:35              

报告地点： 四号楼4318会议室

邀 请人: 潘少华

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数学学院

2023年3月8日

报告摘要：In this work, we consider 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. We first derive the first-order necessary optimality condition by using the first-order operators of the three functions involved. Then we propose first-order algorithms, namely, the proximity-gradient-subgradient algorithm (PGSA). Moreover, we develop PGSA with monotone line search (PGSA_ML), PGSA with nonmonotone line search (PGSA_NL), and PGSA with backtracked extrapolation (PGSA_BE) for possible acceleration. It is shown that any accumulation point of the sequence generated by them is a critical point of the problem under mild assumptions. Global convergence analyses of the sequence are established by the Kurdyka-Lojasiewicz (KL) property of the objective or auxiliary functions. Besides, we show that the KL exponent of the sparse generalized eigenvalue problem associated with a pair of symmetric positive semidefinite matrices is 1/2. Some preliminary numerical experiments on generalized eigenvalue problems and sparse signal recovery problems demonstrate the efficiency of the proposed algorithms.

报告人简介：李洽，中山大学计算机学院副教授、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数据科学系副主任，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，参与项目包括参与国家重点研发计划、国家重大研究计划集成项目、广东省重点研发计划。