报告人：彭拯 教授
报告题目：First-Order Implementations of Cubic Regularized Newton Methods via Momentum and Randomized Smoothing
报告时间：2026年5月26日（周二）晚上7：30
报告地点：腾讯会议：863-688-394
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：
彭拯，湘潭大学教授，博士生导师。主要从事数学优化理论、算法及其应用研究，当前研究兴趣在于流形优化与流形学习、超大规模集成电路EDA、下一代通信网络、新能源电力系统等理论与实际应用中的大规模非凸非光滑优化问题求解算法，尤其关注随机优化算法与非单调优化算法相关研究。主持国家重要科研项目6项，当前兼任中国运筹学会常务理事、湖南省运筹学会副理事长，中国运筹学会算法软件及其应用分会常务理事和数学规划分会理事。
报告摘要：
In this paper, we introduce a randomized second-order scheme for computing second-order stationary points in nonconvex nonsmooth unconstrained optimization. Inspired by the cubic regularized Newton paradigm, the proposed method integrates randomized smoothing with a first-order oracle-based Hessian estimation technique, yielding a tractable approximation of second-order information while avoiding direct evaluations of exact Hessians.
We characterize the relationship between second-order stationarity of the smoothed surrogate problem and (\varepsilon_g,\varepsilon_H)-stationarity of the original nonsmooth problem. Building on this characterization, we establish iteration complexity guarantees for finding (\varepsilon_g,\varepsilon_H,\delta)-second-order stationary points. A momentum mechanism is further embedded into the framework to exploit historical information, stabilize the iterative dynamics, and improve computational efficiency.
