Lyapunov stability of the Euler method
Optimization and Control
2026-02-06 v3
Abstract
We extend the Lyapunov stability criterion to Euler discretizations of differential inclusions. It relies on a pair of Lyapunov functions, one in continuous time and one in discrete time. In the context of optimization, this yields sufficient conditions for the stability of nonisolated local minima when using the Bouligand subgradient method.
Cite
@article{arxiv.2509.11415,
title = {Lyapunov stability of the Euler method},
author = {Cédric Josz},
journal= {arXiv preprint arXiv:2509.11415},
year = {2026}
}