Secant Line Search for Frank-Wolfe Algorithms
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866912421408407552 |
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| author | Hendrych, Deborah Besançon, Mathieu Martínez-Rubio, David Pokutta, Sebastian |
| author_facet | Hendrych, Deborah Besançon, Mathieu Martínez-Rubio, David Pokutta, Sebastian |
| contents | We present a new step-size strategy based on the secant method for Frank-Wolfe algorithms. This strategy, which requires mild assumptions about the function under consideration, can be applied to any Frank-Wolfe algorithm. It is as effective as full line search and, in particular, allows for adapting to the local smoothness of the function, such as in Pedregosa et al 2018, but comes with a significantly reduced computational cost, leading to higher effective rates of convergence. We provide theoretical guarantees and demonstrate the effectiveness of the strategy through numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18775 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Secant Line Search for Frank-Wolfe Algorithms Hendrych, Deborah Besançon, Mathieu Martínez-Rubio, David Pokutta, Sebastian Optimization and Control We present a new step-size strategy based on the secant method for Frank-Wolfe algorithms. This strategy, which requires mild assumptions about the function under consideration, can be applied to any Frank-Wolfe algorithm. It is as effective as full line search and, in particular, allows for adapting to the local smoothness of the function, such as in Pedregosa et al 2018, but comes with a significantly reduced computational cost, leading to higher effective rates of convergence. We provide theoretical guarantees and demonstrate the effectiveness of the strategy through numerical experiments. |
| title | Secant Line Search for Frank-Wolfe Algorithms |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2501.18775 |