AdaptMIO MATH+ AA3-15 â–  completed

Convex Solver Adaptivity for Mixed-Integer Optimization

This project investigates mixed-integer optimization with convex objectives using error-adaptive convex solvers in branch-and-bound. The goal is to develop a faster branch-and-bound methodology by leveraging modern MILP techniques and error-adaptive methods, with key aspects including warm-starting and controlled inexactness in early termination.

Apr 2023 to Mar 2026Apr 23 to Mar 26
4
8

🧑‍🎓 IOL Project Members

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

🤝 External Project Members

Ralf Borndörfer
Principal Investigator
borndoerfer (at) zib.de

🪙 Funding

This project was being funded by the Berlin Mathematics Research Center MATH+ (project ID AA3-15), itself funded by the German Research Foundation (DFG) under Germany's Excellence Strategy (EXC-2046/1, project ID 390685689) from April 2023 to March 2026.

🔬 Project Description

In this project, we aim to investigate mixed-integer optimization problems with a convex, differentiable objective. The focus is on solution approaches based on error-adaptive first-order convex solvers, in particular Frank-Wolfe methods, within a branch-and-bound framework. Our primary objective is to enhance lower bound improvements within the solution tree and analyze the trade-off between the increase in lower bounds and the computational costs of strong relaxations. Our research intends to develop a branch-and-bound-based methodology for mixed-integer convex problems, accelerating the solution process by leveraging the specific characteristics of modern mixed-integer linear programming (MILP) techniques and error-adaptive first-order methods. Two key aspects to be developed and exploited are warm-starting strategies in convex and mixed-integer linear optimization, and early termination methods resulting in the controlled inexactness of certain oracles. Over the course of this project, we develop and maintain a new convex mixed-integer solver written in Julia, named Boscia.jl.

đź’¬ Talks and posters

Conference and workshop talks

Jun 2026
Integer Frank-Wolfe for Optimal Experiment Design by Deborah Hendrych
SIAM conference on optimization (SIAMOP), Edinburgh
Jun 2026
Exact Solutions for the Graph Isomorphism with Convex Mixed Integer Optimization by Wenjie Xiao
SIAM conference on optimization (SIAMOP), Edinburgh
Jun 2026
First-Order Convex (mixed-Integer) Optimization: FrankWolfe.jl and Boscia.jl by Deborah Hendrych
JuMP-dev Workshop (JuMP-dev), Edinburgh [PDF] [video]
May 2026
The Graph Isomorphism Problem From a Mixed-Integer Convex Optimization Perspective by Wenjie Xiao
23rd CPAIOR Conference, Rabat
Sep 2025
Optimal Experiment Design with Mixed-Integer Convex Methods by Deborah Hendrych
16th Global Optimization Workshop (STOGO), Stockholm
Jul 2025
Solving the Optimal Design Problem with Mixed-Integer Convex Methods by Deborah Hendrych
22nd Conference on Advances in Continuous Optimization (EUROPT), Southampton
Jul 2024
Solving the Optimal Design Problem with Mixed-Integer Convex Methods by Deborah Hendrych
22nd Symposium on Experimental Algorithms (SEA), Vienna

Research seminar talks

Jan 2026
Solving the Optimal Design Problem with Mixed-Integer Convex Methods by Deborah Hendrych
Department of Mathematics, Singapore
Mar 2025
Decomposition-Invariant Frank-Wolfe Method in Mixed-Integer Convex Optimization with an Application to Graph Isomorphism by Wenjie Xiao
IOL Research Seminar (IOL), Berlin
Nov 2024
Solving the Optimal Design Problem with Mixed-Integer Convex Methods by Deborah Hendrych
GHOST Research Seminar (GHOST), Grenoble
Jul 2024
Solving the Optimal Design Problem with Mixed-Integer Convex Methods by Deborah Hendrych
NASPDE Seminar, Berlin
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

đź“ť 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}
}
  2. Xiao, W., Hendrych, D., Besançon, M., and Pokutta, S. (2025). Boscia.jl: A review and tutorial. [arXiv]
    [BibTeX]
    @misc{2025_XiaoHendrychBesanconPokutta_Bosciaminlp_2511-01479,
  archiveprefix = {arXiv},
  eprint = {2511.01479},
  arxiv = {arXiv:2511.01479},
  primaryclass = {math.OC},
  year = {2025},
  author = {Xiao, Wenjie and Hendrych, Deborah and Besançon, Mathieu and Pokutta, Sebastian},
  title = {Boscia.jl: A review and tutorial},
  date = {2025-11-03}
}
  3. Zimmer, M., Roux, C., Wagner, M., Hendrych, D., and Pokutta, S. (2025). SparseSwaps: Tractable LLM Pruning Mask Refinement at Scale. [arXiv]
    [BibTeX]
    @misc{2025_ZimmerEtAl_Sparseswapspruning_2512-10922,
  archiveprefix = {arXiv},
  eprint = {2512.10922},
  arxiv = {arXiv:2512.10922},
  primaryclass = {cs.LG},
  year = {2025},
  author = {Zimmer, Max and Roux, Christophe and Wagner, Moritz and Hendrych, Deborah and Pokutta, Sebastian},
  title = {SparseSwaps: Tractable LLM Pruning Mask Refinement at Scale},
  date = {2025-12-11}
}

Conference proceedings

  1. Xiao, W., Besançon, M., Gelß, P., Hendrych, D., Klus, S., and Pokutta, S. (2026). Graph Isomorphism: Mixed-Integer Convex Optimization from First-Order Methods. Lecture Notes in Computer Science, 614–630. DOI: 10.1007/978-3-032-27242-3_36 [arXiv]
    [BibTeX]
    @inproceedings{2025_XiaoEtAl_GraphisomorphismOptimization_2512-17417,
  year = {2026},
  booktitle = {Lecture Notes in Computer Science},
  pages = {614--630},
  doi = {10.1007/978-3-032-27242-3_36},
  archiveprefix = {arXiv},
  eprint = {2512.17417},
  arxiv = {arXiv:2512.17417},
  primaryclass = {math.OC},
  author = {Xiao, Wenjie and Besançon, Mathieu and Gelß, Patrick and Hendrych, Deborah and Klus, Stefan and Pokutta, Sebastian},
  title = {Graph Isomorphism: Mixed-Integer Convex Optimization from First-Order Methods}
}
  2. Troppens, H., Besançon, M., Wilken, S. E., and Pokutta, S. (2025). Mixed-Integer Optimization for Loopless Flux Distributions in Metabolic Networks. Proceedings of the Symposium on Experimental Algorithms, 338, 26:1–26:18. DOI: 10.4230/LIPIcs.SEA.2025.26 [arXiv]
    [BibTeX]
    @inproceedings{2025_TroppensBesanconWilkenPokutta_Mixedintegerloopless,
  year = {2025},
  booktitle = {Proceedings of the Symposium on Experimental Algorithms},
  month = apr,
  volume = {338},
  pages = {26:1--26:18},
  doi = {10.4230/LIPIcs.SEA.2025.26},
  archiveprefix = {arXiv},
  eprint = {2502.00807},
  arxiv = {arXiv:2502.00807},
  primaryclass = {math.OC},
  author = {Troppens, Hannah and Besançon, Mathieu and Wilken, St. Elmo and Pokutta, Sebastian},
  title = {Mixed-Integer Optimization for Loopless Flux Distributions in Metabolic Networks},
  date = {2025-02-02}
}
  3. Hendrych, D., Besançon, M., and Pokutta, S. (2024). Solving the Optimal Experiment Design Problem with Mixed-Integer Convex Methods. Proceedings of the Symposium on Experimental Algorithms, 301, 16:1–16:22. DOI: 10.4230/LIPIcs.SEA.2024.16 [arXiv] [code]
    [BibTeX]
    @inproceedings{2023_HendrychBesanconPokutta_Optimalexperimentdesign,
  year = {2024},
  booktitle = {Proceedings of the Symposium on Experimental Algorithms},
  month = apr,
  volume = {301},
  pages = {16:1--16:22},
  doi = {10.4230/LIPIcs.SEA.2024.16},
  archiveprefix = {arXiv},
  eprint = {2312.11200},
  arxiv = {arXiv:2312.11200},
  primaryclass = {math.OC},
  author = {Hendrych, Deborah and Besançon, Mathieu and Pokutta, Sebastian},
  title = {Solving the Optimal Experiment Design Problem with Mixed-Integer Convex Methods},
  code = {https://github.com/ZIB-IOL/OptimalDesignWithBoscia}
}
  4. Sharma, K., Hendrych, D., Besançon, M., and Pokutta, S. (2024, January 31). Network Design for the Traffic Assignment Problem with Mixed-Integer Frank-Wolfe. Proceedings of the INFORMS Optimization Society Conference. [arXiv]
    [BibTeX]
    @inproceedings{2024_SharmaHendrychBesanconPokutta_NetworkdesignMicoFrankwolfe,
  year = {2024},
  booktitle = {Proceedings of the INFORMS Optimization Society Conference},
  archiveprefix = {arXiv},
  eprint = {2402.00166},
  arxiv = {arXiv:2402.00166},
  primaryclass = {math.OC},
  author = {Sharma, Kartikey and Hendrych, Deborah and Besançon, Mathieu and Pokutta, Sebastian},
  title = {Network Design for the Traffic Assignment Problem with Mixed-Integer Frank-Wolfe},
  date = {2024-01-31}
}

Full articles

  1. 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}
}