【学术报告】Generalized Metric Subregularity with Applications to High-Order Regularized Newton Methods

报告人：朱江醒（云南大学）

时 间：2025年11月20日16:00

地 点：海韵园行政楼C503

内容摘要:

This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our primary focus is on examining this concept concerning first-order and second-order stationary points. We develop an extended convergence framework that enables us to derive superlinear and quadratic convergence under the generalized metric subregularity condition, broadening the widely used KL convergence analysis framework. We present verifiable sufficient conditions to ensure the proposed generalized metric subregularity condition and provide examples demonstrating that the derived convergence rates are sharp. Second, we design a new high-order regularized Newton method with momentum steps, and apply the generalized metric subregularity to establish its superlinear convergence. Quadratic convergence is obtained under additional assumptions. Specifically, when applying the proposed method to solve the (nonconvex) Hadamard reparameterized compressed sensing model, we achieve global convergence with a quadratic local convergence rate towards a global minimizer under a strict complementarity condition.

个人简介：

朱江醒，云南大学数学与统计学院副教授。2015年博士毕业于云南大学。获2024年度云南省自然科学奖一等奖。主要研究方向为变分分析及非光滑优化理论，并主持和参加多项国家自然科学基金。在SIAM Journal on Optimization、 Journal of Optimization Theory and Applications、 Set-Valued and Variational Analysis 、Journal of Global Optimization 等国外知名杂志上发表学术论文20多篇。

联系人：李安