报告题目：New Adaptive Gradient Methods for Convex and Nonconvex Optimization

报 告 人：杨俊锋教授（南京大学）

报告时间：2025年9月26日下午15:30-16:30

报告地点：龙洞校区行政楼 610

Abstract: Consider the unconstrained optimization problem of a continuously differentiable function using the vanilla gradient method. When the objective function is convex and the gradient operator is locally Lipschitz continuous, we propose an adaptive strategy based on the short Barzilai-Borwein step size formula for choosing the step size. The resulting algorithm is line-search-free and parameter-free. We establish the convergence of the iterates and the ergodic convergence of the objective function value. Compared with existing works in this line of research, our algorithm provides the best lower bounds on the step size and the average of the step sizes. Furthermore, we present extensions to the locally strongly convex case and the case of composite convex optimization. Our numerical results also demonstrate the promising potential of the proposed algorithms on some representative examples. We also present an adaptive strategy for choosing the step sizes when the objective function is globally L-smooth but possibly nonconvex.

专家简介：杨俊锋，南京大学数学学院教授，博士生导师、副院长。2009 年 7 月起在南京大学数学学院工作，主要从事最优化计算方法及其应用研究，在 SIAM 系列、Mathematics of OperationsResearch、Mathematics of Computation 等杂志上发表论文40 余篇，开发图像去模糊软代码包FTVd，压缩感知一模解码代码包 YALL1，核磁共振图像复原代码包 RecPF 等。先后主持国家自然科学基金项目 6 项（国家优秀青年基金 1 项，面上项目 3 项，青年项目 1 项，天元访问学者项目 1 项）。获中国运筹学会青年科技奖、入选教育部新世纪优秀人才支持计划等，2020-2023 年连续 4 年入选爱思唯尔中国高被引学者。担任中国运筹学会理事等，担任《计算数学》《ASVAO》《NACO》《SOIC》杂志编委、《Optimization in Engineering》客座编委等。