報告人：彭拯 教授
報告題目：First-Order Implementations of Cubic Regularized Newton Methods via Momentum and Randomized Smoothing
報告時間：2026年5月26日（周二）晚上7：30
報告地點：騰訊會議：863-688-394
主辦單位：數學與統計學院、數學研究院、科學技術研究院
報告人簡介：
彭拯，湘潭大學教授，博士生導師。主要從事數學優化理論、算法及其應用研究，當前研究興趣在于流形優化與流形學習、超大規模集成電路EDA、下一代通信網絡、新能源電力系統等理論與實際應用中的大規模非凸非光滑優化問題求解算法，尤其關注隨機優化算法與非單調優化算法相關研究。主持國家重要科研項目6項，當前兼任中國運籌學會常務理事、湖南省運籌學會副理事長，中國運籌學會算法軟件及其應用分會常務理事和數學規劃分會理事。
報告摘要：
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.