Lyapunov stability of the subgradient method with constant step size

Download PDF
Open Webpage

Cédric Josz, Lexiao Lai

Published: 2023, Last Modified: 25 Jan 2026Math. Program. 2023EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: 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.