Heavy-ball dynamics with Hessian-driven damping for non-convex optimization under the Łojasiewicz condition
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| Format: | Preprint |
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2025
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| author | Apidopoulos, Vassilis Mavrogeorgou, Vasiliki Tsironis, Theodoros G. |
| author_facet | Apidopoulos, Vassilis Mavrogeorgou, Vasiliki Tsironis, Theodoros G. |
| contents | In this paper, we examine the convergence properties of heavy-ball dynamics with Hessian-driven damping in smooth non-convex optimization problems satisfying a Łojasiewicz condition. In this general setting, we provide a series of tight, worst-case optimal convergence rate guarantees as a function of the dynamics' friction coefficients and the Łojasiewicz exponent of the problem's objective function. Importantly, the linear rates that we obtain improve on previous available rates and they suggest a different tuning of the dynamics' damping terms, even in the strongly convex regime. We complement our analysis with a range of stability estimates in the presence of perturbation errors and inexact gradient input, as well as an avoidance result showing that the dynamics under study avoid strict saddle points from almost every initial condition, |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_11705 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Heavy-ball dynamics with Hessian-driven damping for non-convex optimization under the Łojasiewicz condition Apidopoulos, Vassilis Mavrogeorgou, Vasiliki Tsironis, Theodoros G. Optimization and Control 90C26, 34D05, 46N10, 65K05, 65B99 In this paper, we examine the convergence properties of heavy-ball dynamics with Hessian-driven damping in smooth non-convex optimization problems satisfying a Łojasiewicz condition. In this general setting, we provide a series of tight, worst-case optimal convergence rate guarantees as a function of the dynamics' friction coefficients and the Łojasiewicz exponent of the problem's objective function. Importantly, the linear rates that we obtain improve on previous available rates and they suggest a different tuning of the dynamics' damping terms, even in the strongly convex regime. We complement our analysis with a range of stability estimates in the presence of perturbation errors and inexact gradient input, as well as an avoidance result showing that the dynamics under study avoid strict saddle points from almost every initial condition, |
| title | Heavy-ball dynamics with Hessian-driven damping for non-convex optimization under the Łojasiewicz condition |
| topic | Optimization and Control 90C26, 34D05, 46N10, 65K05, 65B99 |
| url | https://arxiv.org/abs/2506.11705 |