MINO MATH+ AA-Mobil-1 ▶ ongoing

Solution Techniques for Mixed-integer Nonconvex Optimization

This project investigates (mixed-)integer optimization with a non-convex, differentiable objective within a Branch-and-Bound framework utilizing Frank-Wolfe methods as node solvers. The focus is on incorporating spatial branching and comparing it to convexification strategies.

Sep 2025 to Aug 2028Sep 25 to Aug 28
3
2

🧑‍🎓 IOL Project Members

Mathieu Besançon
Principal Investigator
Alumni
besancon (at) zib.de
Sebastian Pokutta
Principal Investigator
pokutta (at) zib.de
Deborah Hendrych
hendrych (at) zib.de

🪙 Funding

This project is being funded by the Berlin Mathematics Research Center MATH+ (project ID AA-Mobil-1), itself funded by the German Research Foundation (DFG) under Germany's Excellence Strategy (EXC-2046/1, project ID 390685689) from September 2025 to August 2028.

🔬 Project Description

The project will investigate two main approaches: (1) Automatic Convexification - developing systematic methods to add polynomial terms to objective functions that preserve optimal solutions while making problems more tractable, extending techniques from binary to general integer cases; and (2) Spatial Branching - integrating advanced branching strategies with partial convexification to handle broader problem classes, including parallelization of bound computations and leveraging existing techniques like warm-starting and early termination to improve computational efficiency. The overall goal is to create a comprehensive framework that balances convexification benefits with computational performance through strategic partial convexification and enhanced branching methods.

💬 Talks and posters

Research seminar talks

Jan 2026
Solving the Optimal Design Problem with Mixed-Integer Convex Methods by Deborah Hendrych
Department of Mathematics, Singapore
May 2024
Solving the Optimal Design Problem with Mixed-Integer Convex Methods by Deborah Hendrych
MATH+ Spotlight talks, Berlin
Dec 2023
Solving the Optimal Experiment Design Problems with Mixed-Integer Frank-Wolfe-based Methods by Deborah Hendrych
IOL Research Seminar (IOL), Berlin

Poster presentations

May 2025
Exploiting Combinatorial Algorithms Within Convex Mixed-Integer Optimization by Deborah Hendrych
7th DOxML Conference, Kyoto
Apr 2024
Convex Solver Adaptivity for Mixed-Integer Optimization by Deborah Hendrych
5th Women in Optimization 2024 (WiO), Erlangen

📝 Publications and preprints

Preprints

  1. Mexi, G., Hendrych, D., Designolle, S., Besançon, M., and Pokutta, S. (2025). A Frank-Wolfe-based Primal Heuristic for Quadratic Mixed-integer Optimization. [arXiv]
    [BibTeX]
    @misc{2025_MexiEtAl_Frankwolfeheuristic_2508-01299,
  archiveprefix = {arXiv},
  eprint = {2508.01299},
  arxiv = {arXiv:2508.01299},
  primaryclass = {math.OC},
  year = {2025},
  author = {Mexi, Gioni and Hendrych, Deborah and Designolle, Sébastien and Besançon, Mathieu and Pokutta, Sebastian},
  title = {A Frank-Wolfe-based Primal Heuristic for Quadratic Mixed-integer Optimization},
  date = {2025-08-02}
}

Full articles

  1. Hendrych, D., Troppens, H., Besançon, M., and Pokutta, S. (2025). Convex Integer Optimization with Frank-Wolfe Methods. Mathematical Programming Computation, 17(4), 731–757. DOI: 10.1007/s12532-025-00288-w [URL] [arXiv] [slides] [code]
    [BibTeX]
    @article{2022_HendrychTroppensBesanconPokutta_Convexintegerfrankwolfe,
  year = {2025},
  journal = {Mathematical Programming Computation},
  date = {2025-06-28},
  month = apr,
  volume = {17},
  number = {4},
  pages = {731--757},
  doi = {10.1007/s12532-025-00288-w},
  url = {https://link.springer.com/article/10.1007/s12532-025-00288-w},
  archiveprefix = {arXiv},
  eprint = {2208.11010},
  arxiv = {arXiv:2208.11010},
  primaryclass = {math.OC},
  author = {Hendrych, Deborah and Troppens, Hannah and Besançon, Mathieu and Pokutta, Sebastian},
  title = {Convex Integer Optimization with Frank-Wolfe Methods},
  code = {https://github.com/ZIB-IOL/Boscia.jl},
  slides = {https://pokutta.com/slides/20220915_boscia.pdf}
}