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

IOL Project Members

Mathieu Besançon Principal Investigator · Alumni

Sebastian Pokutta Principal Investigator

Deborah Hendrych Project Member

Karl Welzel Project Member

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

Conference and workshop talks

Jun 2026: First-Order Convex (mixed-Integer) Optimization: FrankWolfe.jl and Boscia.jl by Deborah Hendrych
JuMP-dev Workshop (JuMP-dev), Edinburgh [PDF] [video]

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

Jul 2026: Recent Improvements on the Integer Frank-Wolfe Framework by Deborah Hendrych
ICOML Conference, Taipei
Jul 2026: Recent Improvements on the Integer Frank-Wolfe Framework by Deborah Hendrych
8th DOxML Conference, Tokyo
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

Full articles

Mexi, G., Hendrych, D., Designolle, S., Besançon, M., and Pokutta, S. (2026). A Frank-Wolfe-based primal heuristic for quadratic mixed-integer optimization. Mathematical Programming Computation. DOI: 10.1007/s12532-026-00340-3 [URL] [arXiv] [code]

[BibTeX]

@article{2025_MexiEtAl_Frankwolfeheuristic_2508-01299,
  year = {2026},
  journal = {Mathematical Programming Computation},
  date = {2026-09-03},
  month = sep,
  doi = {10.1007/s12532-026-00340-3},
  url = {https://link.springer.com/article/10.1007/s12532-026-00340-3},
  archiveprefix = {arXiv},
  eprint = {2508.01299},
  arxiv = {arXiv:2508.01299},
  primaryclass = {math.OC},
  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},
  code = {https://github.com/GioniMexi/FW-MIQCQP-Heuristic}
}

Hendrych, D., Troppens, H., Besançon, M., and Pokutta, S. (2025). Convex mixed-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 = dec,
  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 mixed-integer optimization with Frank–Wolfe methods},
  code = {https://github.com/ZIB-IOL/Boscia.jl},
  slides = {https://pokutta.com/slides/20220915_boscia.pdf}
}