2025/11/13 by Huang, Yuyang, Kalise, Dante, Kouhkouh, Hicham
#35Q93 #37N35 #49L12 #90C26 #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2511.10815
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.