Lyapunov stability of the subgradient method with constant step size

• 成果类型: Article
• 署名作者: Josz, Cedric; Lai, Lexiao
• 署名单位: Columbia University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-023-01936-6
• 发表日期: 2023
• 页码: 387-396
• 关键词: stochastic approximations; CONVERGENCE

摘要

We consider the subgradient method with constant step size for minimizing locally Lipschitz semi-algebraic functions. In order to analyze the behavior of its iterates in the vicinity of a local minimum, we introduce a notion of discrete Lyapunov stability and propose necessary and sufficient conditions for stability.