{"ID":2842486,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.10815","arxiv_id":"2511.10815","title":"Non-Convex Global Optimization as an Optimal Stabilization Problem: Dynamical Properties","abstract":"We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set of global minimizers. Specifically, for any tolerance $η\u003e 0$, there exist parameters $λ$ (discount rate) and $t$ (time horizon) such that trajectories remain within an $η$-neighborhood of the global minimizers after some finite time $τ$. This convergence is achieved directly, without solving ergodic Hamilton-Jacobi-Bellman equations. We prove parallel results for three problem formulations: evolutive discounted, stationary discounted, and evolutive non-discounted cases. The analysis relies on occupation measures to quantify the fraction of time trajectories spend away from the minimizer set, establishing both reachability and stability properties.","short_abstract":"We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set of global minimizers. Specifically, for any tolerance $η\u003e 0$, there exist paramet...","url_abs":"https://arxiv.org/abs/2511.10815","url_pdf":"https://arxiv.org/pdf/2511.10815v1","authors":"[\"Yuyang Huang\",\"Dante Kalise\",\"Hicham Kouhkouh\"]","published":"2025-11-13T21:26:07Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[\"Large Language Model\"]","has_code":false}