Non-Convex Global Optimization as an Optimal Stabilization Problem: Convergence Rates
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908918611968000 |
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| author | Huang, Yuyang Kalise, Dante Kouhkouh, Hicham |
| author_facet | Huang, Yuyang Kalise, Dante Kouhkouh, Hicham |
| contents | We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions with multiple global minimizers, where classical gradient-based methods lack global convergence guarantees, we establish explicit exponential convergence rates with computable constants. Our analysis proves (i) variational convergence of the value function of the optimal control problem, (ii) convergence in the objective function for the original problem, as well as (iii) pathwise convergence of optimal trajectories to the minimizer set under minimal structural assumptions that require neither convexity, differentiability, nor Łojasiewicz-type conditions on the objective. These quantitative results significantly strengthen the asymptotic theory developed in our previous work (arXiv:2511.10815). Numerical experiments demonstrate the practical effectiveness of the approach on challenging non-convex problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11122 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Convex Global Optimization as an Optimal Stabilization Problem: Convergence Rates Huang, Yuyang Kalise, Dante Kouhkouh, Hicham Optimization and Control 37N35, 90C26, 49L12, 35Q93 We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions with multiple global minimizers, where classical gradient-based methods lack global convergence guarantees, we establish explicit exponential convergence rates with computable constants. Our analysis proves (i) variational convergence of the value function of the optimal control problem, (ii) convergence in the objective function for the original problem, as well as (iii) pathwise convergence of optimal trajectories to the minimizer set under minimal structural assumptions that require neither convexity, differentiability, nor Łojasiewicz-type conditions on the objective. These quantitative results significantly strengthen the asymptotic theory developed in our previous work (arXiv:2511.10815). Numerical experiments demonstrate the practical effectiveness of the approach on challenging non-convex problems. |
| title | Non-Convex Global Optimization as an Optimal Stabilization Problem: Convergence Rates |
| topic | Optimization and Control 37N35, 90C26, 49L12, 35Q93 |
| url | https://arxiv.org/abs/2511.11122 |