A Quadratically Convergent Semismooth Newton Method for Nonlinear Semidefinite Programming Without Subdifferential Regularity
发布时间:2024年03月26日
浏览次数:965
发布者: Xiaoni Tan
主讲人: Chao Ding(CAS)
活动时间: 从 2024-03-26 14:00 到 15:00
场地: Room 77201, Jingchunyuan 78, BICMR
Abstract: 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.