AA3 – Next Generation Networks



Convex Solver Adaptivity for Mixed-Integer Optimization

Project Heads

Mathieu Besançon (until 12/23), Ralf Borndörfer, Sebastian Pokutta

Project Members

Deborah Hendrych

Project Duration

01.04.2023 – 31.03.2026

Located at



We want to investigate mixed-integer optimization with a convex differentiable objective and solution approaches based on error-adaptive convex solvers in branch-and-bound. We will focus on lower bound improvements within the tree and the tradeoff between the lower bound increase and computational costs of strong relaxations.


We aim to develop a branch-and-bound-based methodology for mixed-integer convex problems that accelerates the solution process by taking advantage of the specificities of modern MILP techniques and error-adaptive first-order methods.

Two aspects that will in particular be developed and exploited are warm-starting in convex and mixed-integer linear optimization, and early termination resulting in the controlled inexactness of some oracles.

Selected Publications

Hendrych, Deborah, Hannah Troppens, Mathieu Besançon, and Sebastian Pokutta. “Convex integer optimization with Frank-Wolfe methods.” arXiv preprint arXiv:2208.11010 (2022).

Software Repositories

The Boscia.jl accompanying arxiv:2208.11010 is available at https://github.com/ZIB-IOL/Boscia.jl and can be installed from the official Julia registry.

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