Convergence of Augmented Lagrangian Methods for Composite Optimization Problems

• 成果类型: Article; Early Access
• 署名作者: Hang, Nguyen Thi Van; Sarabi, Ebrahim
• 署名单位: Nanyang Technological University; Vietnam Academy of Science & Technology (VAST); University System of Ohio; Miami University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.0324
• 发表日期: 2025
• 关键词: local convergence; REGULARITY

摘要

Local convergence analysis of the augmented Lagrangian method (ALM) is established for a large class of composite optimization problems with nonunique Lagrange multipliers under a second-order sufficient condition. We present a new second-order variational property called the semistability of second subderivatives and demonstrate that it is widely satisfied for numerous classes of functions, which is important for applications in constrained and composite optimization problems. Using the latter condition and a certain second-order sufficient condition, we are able to establish Q-linear convergence of the primal-dual sequence for an inexact version of the ALM for composite programs.