Lyapunov stability of the subgradient method with constant step size

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.

11 pages, 2 figures

Cited by in corpus (1)

• A subgradient method with constant step-size for ${\ell }_1$-composite optimization