报告题目：Halpern Acceleration of the Inexact Proximal Point Method of Rockafellar

报 告 人：张立卫教授（东北大学智能工业与系统优化国家级前沿科学研究中心）

报告时间：2026年10月23日（周五）上午9：00-10：00

报告地点：腾讯会议号：950947782

主  持  人：刘玉兰

报告摘要：This work investigates a Halpern acceleration of the inexact proximal point method of Rockafellar for solving maximal monotone inclusion problems in Hilbert spaces. The proposed Halpern inexact proximal point method (HiPPM) is shown to be globally convergent, and a unified framework is developed to analyze its worst case convergence behavior. Under mild conditions on the inexactness tolerances, HiPPM achieves an O() convergence rate in terms of the squared fixed point residual. Moreover, under additional well-studied regularity conditions, the method attains a fast linear convergence rate. Building on this framework, we further extend the Halpern acceleration to the inexact augmented Lagrangian method for constrained convex optimization. In the spirit of Rockafellar’s classical results, the resulting accelerated inexact augmented Lagrangian method inherits the convergence rate and iteration complexity guarantees of HiPPM.Numerical experiments are provided to support the theoretical findings.

个人简介：张立卫，东北大学智能工业与系统优化国家级前沿科学研究中心教授，中国运筹学会监事。长期从事“矩阵优化”，“随机规划”和“均衡优化”的理论与算法的研究。在专业期刊上发表SCI检索论文130多篇, 其中包括在国际顶级期刊Mathematical Programming, Operations Research, SIAM Journal on Optimization, Mathematics of Operations Research, Mathematics of Computation, JMLR, IEEE Transactions on Automatic Control 发表论文二十余篇。在科学出版社出版专著和教材6部。他目前主持一项国家重点研发计划课题，完成和主持自然科学基金面上基金多项,重点基金子课题两项。《JAPOR》,《NACO》和《运筹学学报》编委，2020年获得中国运筹学会运筹研究奖。