Lyapunov stability of the subgradient method with constant step size
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Abstract (arXiv)
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.
Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Nov 2022.
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Citing papers per year: 2023: 1; 2024: 3; 2025: 0; 2026: 1.
5 papers.
- 2023Stochastic Subgradient Methods with Guaranteed Global Stability in Nonsmooth Nonconvex Optimizationcited by 3
- 2024Developing Lagrangian-based Methods for Nonsmooth Nonconvex Optimizationcited by 2
- 2024Convergence of Decentralized Stochastic Subgradient-based Methods for Nonsmooth Nonconvex functionscited by 1
- 2024Inexact subgradient methods for semialgebraic functionscited by 1
- 2026Decentralized Stochastic Subgradient-type Methods with Communication Compression for Nonsmooth Nonconvex Optimizationcited by 0
- 2026Decentralized Stochastic Subgradient-type Methods with Communication Compression for Nonsmooth Nonconvex Optimization2 Jul 2026
- 2024Inexact subgradient methods for semialgebraic functions30 Apr 2024
- 2024Developing Lagrangian-based Methods for Nonsmooth Nonconvex Optimization15 Apr 2024
- 2024Convergence of Decentralized Stochastic Subgradient-based Methods for Nonsmooth Nonconvex functions18 Mar 2024
- 2023Stochastic Subgradient Methods with Guaranteed Global Stability in Nonsmooth Nonconvex Optimization19 Jul 2023