The paper “Convex mixed-integer optimization with Frank–Wolfe methods” by Deborah Hendrych, Hannah Troppens, Mathieu Besançon, and Sebastian Pokutta, from the Interactive Optimization at Learning Lab at ZIB and TU Berlin, has been selected as the Outstanding Paper of the Year 2025 of Mathematical Programming Computation (MPC), the leading journal for computational mathematical optimization, published in cooperation with the Mathematical Optimization Society. Mathieu Besançon has since joined Inria center at the Université Grenoble Alpes as a faculty member.
Mixed-integer nonlinear optimization encompasses a broad class of problems that present both theoretical and computational challenges. The award-winning paper proposes a new type of method for these problems, based on a branch-and-bound algorithm with convex node relaxations. The 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 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. The image presents a schematic of the new method which is available as the open-source Julia package Boscia.jl.
The research was funded by Cluster of Excellence Math+ and the research campus MODAL.
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