# Lyapunov stability of the subgradient method with constant step size

arXiv: https://arxiv.org/abs/2211.14850 · HTML: https://mlsanity.com/paper/2211.14850/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2022.

## Built on by (most cited first, 5 of 5)

- [Stochastic Subgradient Methods with Guaranteed Global Stability in Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2307.10053/) (2023)
- [Developing Lagrangian-based Methods for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2404.09438/) (2024)
- [Convergence of Decentralized Stochastic Subgradient-based Methods for Nonsmooth Nonconvex functions](https://mlsanity.com/paper/2403.11565/) (2024)
- [Inexact subgradient methods for semialgebraic functions](https://mlsanity.com/paper/2404.19517/) (2024)
- [Decentralized Stochastic Subgradient-type Methods with Communication Compression for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2607.01755/) (2026)

## 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.