Matthias Walter

I am an assistant professor at University of Twente in the Discrete Mathematics & Mathematical Programming group. I received my Ph.D. in Magdeburg under supervision of Volker Kaibel and worked as a postdoctoral researcher at RWTH Aachen University in the group of Marco Lübbecke. My fields of interest are mixed-integer linear optimization, polyhedral combinatorics and computational matroid theory.

You can reach me via email or snail mail.

Research Forschung

Here you can find some research and projects of mine.

Polyhedral Combinatorics

The goal of this field is to understand polyhedra that are associated to combinatorial or mixed-integer linear optimization problems.

Investigating Polyhedra by Oracles

A software for analyzing the structures of polyhedra that are implicitly defined by optimization oracles.

Combinatorial Matrix Recognition Library

A matrix is TU if all its subdeterminants are -1, 0, +1, which is an important property in mixed-integer programming. This and related properties can be checked efficiently using this software.

Teaching Lehre

Mixed-integer Optimization

Lecture: 3rd quartile 2023/2024

Integer Programming Methods

Lecture: 2nd LNMB trimester 2023/2024

Python Programming

Lectorial: 1st, 3rd and 4th quartile 2023/2024

Publications Publikationen

With: Alberto Del Pia.
Simple Odd β-Cycle Inequalities for Binary Polynomial Optimization.
In Karen Aardal and Laura Sanità, editors, Integer Programming and Combinatorial Optimization, pages 181-194. Springer International Publishing, 2022.
The Graphical Traveling Salesperson Problem has no integer programming formulation in the original space.
Operations Research Letters, 49(4):623-624, 2021.
Face Dimensions of General-Purpose Cutting Planes for Mixed-Integer Linear Programs.
In Mohit Singh and David P. Williamson, editors, Integer Programming and Combinatorial Optimization, pages 399-412. Springer International Publishing, 2021.
With: Elisabeth Rodríguez-Heck, Karl Stickler, and Stefan Weltge.
Persistency of Linear Programming Relaxations for the Stable Set Problem.
Integer Programming and Combinatorial Optimization: 21st International Conference, IPCO 2020, London, UK, June 8--10, 2020, Proceedings, pages 351.2020.
With: Marije Siemann.
A Polyhedral Study for the Cubic Formulation of the Unconstrained Traveling Tournament Problem.
COMMENT, arXiv, 2020.
With: Stefan Weltge.
Extended formulations for radial cones.
Operations Research Letters, 47(5):458-463, 2019.
Complete Description of Matching Polytopes with One Linearized Quadratic Term for Bipartite Graphs.
SIAM Journal on Discrete Mathematics, 33(2):1061-1094, 2019.
With: Dominik Ermel.
Parity polytopes and binarization.
Discrete Applied Mathematics, 2018.
With: Volker Kaibel.
A Note on Matchings Constructed during Edmonds' Weighted Perfect Matching Algorithm.
Note, arXiv, 2017.
With: Pelin Damcı-Kurt, Santanu S. Dey, and Simge Küçükyavuz.
On a cardinality-constrained transportation problem with market choice.
Operations Research Letters, 44(2):170-173, 2016.
With: Volker Kaibel.
Investigating Polyhedra by Oracles.
Integer Programming and Combinatorial Optimization, 18th International Conference, IPCO 2016, Liège, Belgium, June 1-3, 2016. Poster presentation, 2016.
Investigating Polyhedra by Oracles and Analyzing Simple Extensions of Polytopes.
Dissertation, Otto-von-Guericke-Universität Magdeburg, 2016.
With: Volker Kaibel, Jon Lee, and Stefan Weltge.
Extended Formulations for Independence Polytopes of Regular Matroids.
Graphs and Combinatorics, 32(5):1931-1944, 2016.
With: Volker Kaibel.
Simple extensions of polytopes.
Math. Program. Ser. B, 154(1-2):381-406, 2015.
With: Michele Conforti, Volker Kaibel, and Stefan Weltge.
Subgraph polytopes and independence polytopes of count matroids.
Operations Research Letters, 43(5):457-460, 2015.
With: Nils Wegmann.
Computational Study of Graphic TSP Approximation Algorithms.
Integer Programming and Combinatorial Optimization, 17th International Conference, IPCO 2014, Bonn, Germany, June 23-25, 2014. Poster presentation, 2014.
With: Klaus Truemper.
Implementation of a unimodularity test.
Math. Program. Ser. C, 5(1):57-73, 2013.
Sparsity of Lift-and-Project Cutting Planes.
In Stefan Helber, Michael Breitner, Daniel Rösch, Cornelia Schön, Johann-Matthias Graf von der Schulenburg, Philipp Sibbertsen, Marc Steinbach, Stefan Weber, and Anja Wolter, editors, Operations Research Proceedings 2012, pages 9-14. Springer International Publishing, 2012.
Sparsity of Lift-and-Project Cutting Planes.
Diploma thesis, Otto-von-Guericke-Universität Magdeburg, 2011.

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For detecting certain software

Matthias Walter

Research Forschung

Polyhedral Combinatorics

Polyedrische Kombinatorik

Investigating Polyhedra by Oracles

Investigating Polyhedra by Oracles

Combinatorial Matrix Recognition Library

Combinatorial Matrix Recognition Library

Teaching Lehre

Mixed-integer Optimization

Mixed-integer Optimization

Integer Programming Methods

Integer Programming Methods

Python Programming

Python Programming

Publications Publikationen

Tools Tools

LaTeX Resources

LaTeX Ressourcen

CMake Modules

CMake Module