{"ID":2871447,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.11415","arxiv_id":"2509.11415","title":"Lyapunov stability of the Euler method","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.","short_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 Bouli...","url_abs":"https://arxiv.org/abs/2509.11415","url_pdf":"https://arxiv.org/pdf/2509.11415v3","authors":"[\"Cédric Josz\"]","published":"2025-09-14T20:08:15Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[\"Generative Adversarial Network\"]","has_code":false}