报告题目 (Title)：A quadratically convergent semismooth Newton method for nonlinear semidefinite programming without subdifferential regularity
报告人 (Speaker)：郦旭东 教授（复旦大学）
报告时间 (Time)：2024年10月25日 (周六) 10:00-12:00
报告地点 (Place)：校本部 乐乎新楼 大学厅
邀请人(Inviter)：徐 姿 教授
主办部门：永利数学系
报告摘要：
The non-singularity of generalized Jacobians of the Karush-Kuhn-Tucker (KKT) system is crucial for local convergence analysis of semismooth Newton methods. In this talk, we present a new approach that challenges this conventional requirement. Our discussion revolves around a methodology that leverages some newly developed variational properties, effectively bypassing the necessity for non-singularity of all elements in the generalized Jacobian. Quadratic convergence results of our Newton methods are established without relying on commonly assumed subdifferential regularity conditions. This discussion may offer fresh insights into semismooth Newton methods, potentially paving the way for designing robust and efficient second-order algorithms for general nonsmooth composite optimizations.
