Non-Convex Global Optimization as an Optimal Stabilization Problem: Dynamical Properties
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915616645971968 |
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| author | Huang, Yuyang Kalise, Dante Kouhkouh, Hicham |
| author_facet | Huang, Yuyang Kalise, Dante Kouhkouh, Hicham |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10815 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Convex Global Optimization as an Optimal Stabilization Problem: Dynamical Properties Huang, Yuyang Kalise, Dante Kouhkouh, Hicham Optimization and Control 37N35, 90C26, 49L12, 35Q93 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. |
| title | Non-Convex Global Optimization as an Optimal Stabilization Problem: Dynamical Properties |
| topic | Optimization and Control 37N35, 90C26, 49L12, 35Q93 |
| url | https://arxiv.org/abs/2511.10815 |