讲座题目：面向凸优化与非凸优化的新型自适应梯度方法

讲座专家：杨俊锋

讲座时间：2025年9月14日（周日）下午15:00

讲座地点：天府校区雁归楼3017

报告摘要：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、博导；河北省邢台市威县人，2003年在河北师范大学数学系获学士学位，2009年在南京大学数学系获博士学位，先后在中国科学院数学与系统科学研究院、Rice大学联合培养；2009年7月起在南京大学数学系工作至今，期间先后在新加坡国立大学、香港中文大学等访学；主要从事数学优化计算方法及其应用研究，代表作发表在Math. Comput.、Math. Oper. Res.、SIOPT、SISC、SIIMS、JSC、Inverse Prob.、IEEE J Sel Top Signal Process等杂志，设计完成图像复原代码包FTVd、压缩感知解码包YALL1等；入选教育部新世纪优秀人才支持计划、获中国运筹学会青年科技奖、2020至2024年5次入选爱思唯尔中国高被引学者等，先后主持国家自然科学基金青年、面上、优青等项目。现担任中国运筹学会理事、江苏省运筹学会监事长、民建江苏省委员会大数据与人工智能委员会委员等；担任Applied Set-Valued Analysis and Optimization (ASVAO)、Numerical Algebra, Control and Optimization (NACO)、Statistics, Optimization and Information Computing (SOIC)、《计算数学》编委，Optimization and Engineering客座编委等。