报告人：杨俊锋 教授
报告题目：Tight Sublinear Convergence Rate of the Proximal Point Algorithm
报告时间：2026年10月16日（周五）下午2：00 - 4：00
报告地点：云龙校区智华楼405室
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
杨俊锋，南京大学数学学院教授，博士生导师，副院长。中国运筹学会理事、江苏省运筹学会监事长。 先后师从中国科学院袁亚湘院士、南京大学何炳生教授、莱斯大学张寅教授。2009年7月起在南京大学数学学院工作至今，主要从事最优化计算方法及其应用研究，代表作发表于SIAM系列、MOR、Mathematics of Computation等杂志，先后主持国家自然科学基金项目多项，2016年获中国运筹学会青年科技奖。
报告摘要：
Tight sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems is established based on the squared fixed point residual. By using the performance estimation framework, the tight sublinear convergence rate problem is written as an infinite dimensional nonconvex optimization problem, which is then equivalently reformulated as a finite dimensional semidefinite programming (SDP) problem. By solving the SDP, exact sublinear rate is computed numerically. Theoretically, by constructing a feasible solution to the dual SDP, an upper bound is obtained for the tight sublinear rate, and, on the other hand, an example in two dimensional space is constructed to provide a lower bound. The lower bound matches exactly the upper bound obtained from the dual SDP, which also coincides with the numerical rate computed. Hence, we have established the worst case sublinear convergence rate, which is tight in terms of both the order and the constants involved. (joint work with Prof. Guoyong Gu)
