Convex mixed-integer optimization with Frank-Wolfe methods
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866916328903802880 |
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| author | Hendrych, Deborah Troppens, Hannah Besançon, Mathieu Pokutta, Sebastian |
| author_facet | Hendrych, Deborah Troppens, Hannah Besançon, Mathieu Pokutta, Sebastian |
| contents | Mixed-integer nonlinear optimization encompasses a broad class of problems that present both theoretical and computational challenges. We propose a new type of method to solve these problems based on a branch-and-bound algorithm with convex node relaxations. These relaxations are solved with a Frank-Wolfe algorithm over the convex hull of mixed-integer feasible points instead of the continuous relaxation via calls to a mixed-integer linear solver as the linear minimization oracle. The proposed method computes feasible solutions while working on a single representation of the polyhedral constraints, leveraging the full extent of mixed-integer linear solvers without an outer approximation scheme and can exploit inexact solutions of node subproblems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_11010 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Convex mixed-integer optimization with Frank-Wolfe methods Hendrych, Deborah Troppens, Hannah Besançon, Mathieu Pokutta, Sebastian Optimization and Control Discrete Mathematics Machine Learning Computation Mixed-integer nonlinear optimization encompasses a broad class of problems that present both theoretical and computational challenges. We propose a new type of method to solve these problems based on a branch-and-bound algorithm with convex node relaxations. These relaxations are solved with a Frank-Wolfe algorithm over the convex hull of mixed-integer feasible points instead of the continuous relaxation via calls to a mixed-integer linear solver as the linear minimization oracle. The proposed method computes feasible solutions while working on a single representation of the polyhedral constraints, leveraging the full extent of mixed-integer linear solvers without an outer approximation scheme and can exploit inexact solutions of node subproblems. |
| title | Convex mixed-integer optimization with Frank-Wolfe methods |
| topic | Optimization and Control Discrete Mathematics Machine Learning Computation |
| url | https://arxiv.org/abs/2208.11010 |