Generalized Metric Subregularity with Applications to High-Order Regularized Newton Methods

• 成果类型: Article; Early Access
• 署名作者: Li, Guoyin; Mordukhovich, Boris; Zhu, Jiangxing
• 署名单位: University of New South Wales Sydney; Wayne State University; Yunnan University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2024.0570
• 发表日期: 2026-04-07
• 关键词: variational analysis and optimization; generalized metric subregularity; error bounds; high-order regularized Newton methods; Kurdyka-& Lstrok; ojasiewicz property; superlinear and quadratic convergence; cubic regularization; STABLE MINIMIZERS; CONVERGENCE; algorithms

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 Kurdyka-& Lstrok;ojasiewicz (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 toward a global minimizer under a strict complementarity condition.