Convex mixed-integer optimization with Frank–Wolfe methods

  • 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.

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Metadaten
Author:Deborah HendrychORCiD, Hannah TroppensORCiD, Mathieu BesançonORCiD, Sebastian PokuttaORCiD
DOI:https://doi.org/10.1007/s12532-025-00288-w
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2025
Volume:17
Issue:4
Page Number:27
First Page:731
Last Page:757
Mathematical Programming Computation :MPC 2025 - Issue 4
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