数学科学学院学术报告
First-Order Algorithms for Single-Ratio Minimization Problems
李洽
（中山大学）
报告时间：2024年12月06日 周五 上午 09:00-10:00
报告地点：腾讯会议：382-838-649 会议密码：1206
报告摘要：In this talk, we focus on a class of single-ratio minimization problems, where the numerator of the objective is the sum of a nonsmooth nonconvex function f and a smooth nonconvex function h, while the denominator g is a nonsmooth convex function. We analyze the first-order necessary optimality condition and propose the Proximity-Gradient-Subgradient Algorithm (PGSA), along with its modified version, PGSA_L, which incorporates a line-search scheme. Specifically, when f is convex, we implement a backtracked extrapolation technique to enhance PGSA. Besides, for cases where f is block-separable, we present a novel reformulation of the problem and propose a solving framework called multi-proximity gradient algorithm (MPGA). We establish subsequential convergence analysis for all the proposed algorithms. Moreover, the global convergence is established by the Kurdyka-Łojasiewicz (KL) property of auxiliary functions and some mild additional assumptions. Furthermore, we prove that in several special cases of fractional programs, the corresponding KL exponents are 1/2, which leads to linear convergence rates for the proposed algorithms. Finally, some preliminary numerical results demonstrate the efficiency of our 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，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常务理事兼副秘书长，广东省计算科学重点实验室成员。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。研究方向包括最优化理论与算法及在机器学习、大数据分析、图像处理等领域中的应用，研究成果发表于SIAM Journal on Optimization, Applied and Computational Harmonic Analysis, Mathematics of Operations Research, Inverse Problems等期刊，其中一篇论文被评为2017年Inverse Problems 期刊Highlights论文。主持国家级科研项目四项（包括国基面上两项、国基青年与GF类项目一项），参与项目包括国基重大研究计划集成项目，科技部重大专项等。
邀请人：谢家新
