A quadratically convergent semismooth Newton method for nonlinear semidefinite programming without subdifferential regularity

报告题目：A quadratically convergent semismooth Newton method for nonlinear semidefinite programming without subdifferential regularity

报告人：郦旭东  青年研究员（复旦大学）

主持人：王祥丰  副教授

报告时间：2024年3月18日（星期一）15:00-16:00

报告地点：华东师范大学普陀校区理科楼B112

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.

报告人简介：

       郦旭东，复旦大学大数据学院青年研究员，主要关注数据科学中的大规模优化问题的理论、算法及应用，现为 Mathematical Programming Computation AE。