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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.20370 |
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| _version_ | 1866913039817637888 |
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| author | Oikonomidis, Konstantinos Bodard, Alexander Quan, Jan Patrinos, Panagiotis |
| author_facet | Oikonomidis, Konstantinos Bodard, Alexander Quan, Jan Patrinos, Panagiotis |
| contents | We study a continuous-time dynamical system which arises as the limit of a broad class of nonlinearly preconditioned gradient methods. Under mild assumptions, we establish existence of global solutions and derive Lyapunov-based convergence guarantees. For convex costs, we prove a sublinear decay in a geometry induced by some reference function, and under a generalized gradient-dominance condition we obtain exponential convergence. We further uncover a duality connection with mirror descent, and use it to establish that the flow of interest solves an infinite-horizon optimal-control problem of which the value function is the Bregman divergence generated by the cost. These results clarify the structure and optimization behavior of nonlinearly preconditioned gradient flows and connect them to known continuous-time models in non-Euclidean optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20370 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinearly preconditioned gradient flows Oikonomidis, Konstantinos Bodard, Alexander Quan, Jan Patrinos, Panagiotis Optimization and Control Dynamical Systems We study a continuous-time dynamical system which arises as the limit of a broad class of nonlinearly preconditioned gradient methods. Under mild assumptions, we establish existence of global solutions and derive Lyapunov-based convergence guarantees. For convex costs, we prove a sublinear decay in a geometry induced by some reference function, and under a generalized gradient-dominance condition we obtain exponential convergence. We further uncover a duality connection with mirror descent, and use it to establish that the flow of interest solves an infinite-horizon optimal-control problem of which the value function is the Bregman divergence generated by the cost. These results clarify the structure and optimization behavior of nonlinearly preconditioned gradient flows and connect them to known continuous-time models in non-Euclidean optimization. |
| title | Nonlinearly preconditioned gradient flows |
| topic | Optimization and Control Dynamical Systems |
| url | https://arxiv.org/abs/2511.20370 |