Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.13910 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916655376891904 |
|---|---|
| author | Aal, Osama F. Abdel Ozbek, Necdet Sinan Viola, Jairo Chen, YangQuan |
| author_facet | Aal, Osama F. Abdel Ozbek, Necdet Sinan Viola, Jairo Chen, YangQuan |
| contents | From the perspective of control theory, the gradient descent optimization methods can be regarded as a dynamic system where various control techniques can be designed to enhance the performance of the optimization method. In this paper, we propose a prescribed finite-time convergent gradient flow that uses time-varying gain nonlinear feedback that can drive the states smoothly towards the minimum. This idea is different from the traditional finite-time convergence algorithms that relies on fractional-power or signed gradient as a nonlinear feedback, that is proved to have finite/fixed time convergence satisfying strongly convex or the Polyak-Łojasiewicz (PŁ) inequality, where due to its nature, the proposed approach was shown to achieve this property for both strongly convex function, and for those satisfies Polyak-Łojasiewic inequality. Our method is proved to converge in a prescribed finite time via Lyapunov theory. Numerical experiments were presented to illustrate our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13910 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Controlled Optimization with a Prescribed Finite-Time Convergence Using a Time Varying Feedback Gradient Flow Aal, Osama F. Abdel Ozbek, Necdet Sinan Viola, Jairo Chen, YangQuan Optimization and Control From the perspective of control theory, the gradient descent optimization methods can be regarded as a dynamic system where various control techniques can be designed to enhance the performance of the optimization method. In this paper, we propose a prescribed finite-time convergent gradient flow that uses time-varying gain nonlinear feedback that can drive the states smoothly towards the minimum. This idea is different from the traditional finite-time convergence algorithms that relies on fractional-power or signed gradient as a nonlinear feedback, that is proved to have finite/fixed time convergence satisfying strongly convex or the Polyak-Łojasiewicz (PŁ) inequality, where due to its nature, the proposed approach was shown to achieve this property for both strongly convex function, and for those satisfies Polyak-Łojasiewic inequality. Our method is proved to converge in a prescribed finite time via Lyapunov theory. Numerical experiments were presented to illustrate our results. |
| title | Controlled Optimization with a Prescribed Finite-Time Convergence Using a Time Varying Feedback Gradient Flow |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.13910 |