Global stability of first-order methods for coercive tame functions

• 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/s10107-023-02020-9
• 发表日期: 2024
• 页码: 551-576
• 关键词: stochastic approximations; differential-inclusions; CONVERGENCE

摘要

We consider first-order methods with constant step size for minimizing locally Lipschitz coercive functions that are tame in an o-minimal structure on the real field. We prove that if the method is approximated by subgradient trajectories, then the iterates eventually remain in a neighborhood of a connected component of the set of critical points. Under suitable method-dependent regularity assumptions, this result applies to the subgradient method with momentum, the stochastic subgradient method with random reshuffling and momentum, and the random-permutations cyclic coordinate descent method.