A Frank-Wolfe Algorithm for Strongly Monotone Variational Inequalities
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866914075447918592 |
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| author | Baghbadorani, Reza Rahimi Esfahani, Peyman Mohajerin Grammatico, Sergio |
| author_facet | Baghbadorani, Reza Rahimi Esfahani, Peyman Mohajerin Grammatico, Sergio |
| contents | We propose an accelerated algorithm with a Frank-Wolfe method as an oracle for solving strongly monotone variational inequality problems. While standard solution approaches, such as projected gradient descent (aka value iteration), involve projecting onto the desired set at each iteration, a distinctive feature of our proposed method is the use of a linear minimization oracle in each iteration. This difference potentially reduces the projection cost, a factor that can become significant for certain sets or in high-dimensional problems. We validate the performance of the proposed algorithm on the traffic assignment problem, motivated by the fact that the projection complexity per iteration increases exponentially with respect to the number of links. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03842 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Frank-Wolfe Algorithm for Strongly Monotone Variational Inequalities Baghbadorani, Reza Rahimi Esfahani, Peyman Mohajerin Grammatico, Sergio Optimization and Control We propose an accelerated algorithm with a Frank-Wolfe method as an oracle for solving strongly monotone variational inequality problems. While standard solution approaches, such as projected gradient descent (aka value iteration), involve projecting onto the desired set at each iteration, a distinctive feature of our proposed method is the use of a linear minimization oracle in each iteration. This difference potentially reduces the projection cost, a factor that can become significant for certain sets or in high-dimensional problems. We validate the performance of the proposed algorithm on the traffic assignment problem, motivated by the fact that the projection complexity per iteration increases exponentially with respect to the number of links. |
| title | A Frank-Wolfe Algorithm for Strongly Monotone Variational Inequalities |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.03842 |