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arXiv · 2511.10815

Non-Convex Global Optimization as an Optimal Stabilization Problem: Dynamical Properties

Yuyang Huang·Dante Kalise·Hicham Kouhkouh
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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 $η> 0$, 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.

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Yuyang Huang, Dante Kalise, Hicham Kouhkouh. 2025-11-13. Non-Convex Global Optimization as an Optimal Stabilization Problem: Dynamical Properties. https://arxiv.org/abs/2511.10815

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