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.
Sufficient conditions for instability of the subgradient method with constant step size
Iteration-Complexity of the Subgradient Method on Riemannian Manifolds with Lower Bounded Curvature
Subgradient methods near active manifolds: saddle point avoidance, local convergence, and asymptotic normality
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