Convex mixed-integer optimization with Frank-Wolfe methods
Abstract
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.
Cite
@article{arxiv.2208.11010,
title = {Convex mixed-integer optimization with Frank-Wolfe methods},
author = {Deborah Hendrych and Hannah Troppens and Mathieu Besançon and Sebastian Pokutta},
journal= {arXiv preprint arXiv:2208.11010},
year = {2024}
}