Chenglong Bao, Associate Professor, Tsinghua University

Haijun Yu, Professor

An Optimal Regularized Newton Method for Non-Convex Optimization

14:00-15:00 October 22(Wednesday), N226

This talk presents an adaptive regularized Newton method for solving nonconvex optimization problems. The proposed algorithm is parameter-free and does not require prior knowledge of the Hessian Lipschitz constant. From a theoretical perspective, we establish both optimal global complexity and local quadratic convergence. This result bridges the gap between global complexity guarantees and fast local convergence. Numerical experiments demonstrate the advantages of the method, including applications to training PINNs, where it achieves substantially lower training loss for solving various classes of PDEs.

报告人简介：包承龙，清华大学丘成桐数学科学中心长聘副教授、北京雁栖湖应用数学研究院副教授、清华大学膜生物学全国重点实验室研究员。研究兴趣主要在人工智能、图像处理和最优化算法方面，已在Nat. Commun., SIAM系列、IEEE TPAMI等各类期刊和会议上发表学术论文60余篇。