Mathematical Data Analytics

Research

The focus of our research is on the mathematical foundations of optimization. We are particularly interested in structural and complexity questions arising from discrete optimization and discrete geometry.

Head

$TO$

Prof. Dr. Timm Oertel

Professorship for Mathematical Data Analytics

Head

Contact

Email: timm.oertel@fau.de
Phone: +49 9131 85-67313

Team

Nicola Wengiel

Professorship for Mathematical Data Analytics

Research associates

Contact

Email: nicola.wengiel@fau.de

Bachelor and Master theses

I am happy to discuss possible topics.

Publications

2025

Kuhlmann S., Oertel T., Weismantel R.:
Sparse Approximation in Lattices and Semigroups
26th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2025 (Baltimore, MD, USA, 11.06.2025 - 13.06.2025)
In: Nicole Megow, Amitabh Basu (ed.): Lecture Notes in Computer Science 2025
DOI: 10.1007/978-3-031-93112-3_27
BibTeX: Download

2024

Aliev I., Henk M., Hogan M., Kuhlmann S., Oertel T.:
New Bounds for the Integer Carathéodory Rank
In: SIAM Journal on Optimization 34 (2024), p. 190-200
ISSN: 1052-6234
DOI: 10.1137/23M1561312
BibTeX: Download

2023

Oertel T., Paat J., Weismantel R.:
A colorful Steinitz Lemma with application to block-structured integer programs
In: Mathematical Programming (2023)
ISSN: 0025-5610
DOI: 10.1007/s10107-023-01971-3
BibTeX: Download

2021

Aliev I., Averkov G., De Loera JA., Oertel T.:
Sparse representation of vectors in lattices and semigroups
In: Mathematical Programming (2021)
ISSN: 0025-5610
DOI: 10.1007/s10107-021-01657-8
BibTeX: Download

2020

Aliev I., Averkov G., De Loera JA., Oertel T.:
Optimizing Sparsity over Lattices and Semigroups
21st International Conference on Integer Programming and Combinatorial Optimization, IPCO 2020 (London, 08.06.2020 - 10.06.2020)
In: Daniel Bienstock, Giacomo Zambelli (ed.): Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 2020
DOI: 10.1007/978-3-030-45771-6_4
BibTeX: Download
Aliev I., Henk M., Oertel T.:
Distances to lattice points in knapsack polyhedra
In: Mathematical Programming 182 (2020), p. 175-198
ISSN: 0025-5610
DOI: 10.1007/s10107-019-01392-1
BibTeX: Download
Oertel T., Paat J., Weismantel R.:
The distributions of functions related to parametric integer optimization
In: SIAM Journal on Applied Algebra and Geometry 4 (2020), p. 422-440
ISSN: 2470-6566
DOI: 10.1137/19M1275954
BibTeX: Download

2019

Oertel T., Paat J., Weismantel R.:
Sparsity of Integer Solutions in the Average Case
20th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2019 (Ann Arbor, MI, 22.05.2019 - 24.05.2019)
In: Andrea Lodi, Viswanath Nagarajan (ed.): Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 2019
DOI: 10.1007/978-3-030-17953-3_26
BibTeX: Download

2018

Aliev I., De Loera JA., Eisenbrand F., Oertel T., Weismantel R.:
The support of integer optimal solutions
In: SIAM Journal on Optimization 28 (2018), p. 2152-2157
ISSN: 1052-6234
DOI: 10.1137/17M1162792
BibTeX: Download

2017

Aliev I., De Loera JA., Oertel T., O'Neill C.:
Sparse solutions of linear diophantine equations
In: SIAM Journal on Applied Algebra and Geometry 1 (2017), p. 239-253
ISSN: 2470-6566
DOI: 10.1137/16M1083876
BibTeX: Download
Aliev I., Henk M., Oertel T.:
Integrality gaps of integer knapsack problems
19th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2017 (Waterloo, ON, CAN, 26.06.2017 - 28.06.2017)
In: Friedrich Eisenbrand, Jochen Koenemann (ed.): Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 2017
DOI: 10.1007/978-3-319-59250-3_3
BibTeX: Download
Basu A., Oertel T.:
Centerpoints: A link between optimization and convex geometry
In: SIAM Journal on Optimization 27 (2017), p. 866-889
ISSN: 1052-6234
DOI: 10.1137/16M1092908
BibTeX: Download

2016

Artmann S., Eisenbrand F., Glanzer C., Oertel T., Vempala S., Weismantel R.:
A note on non-degenerate integer programs with small sub-determinants
In: Operations Research Letters 44 (2016), p. 635-639
ISSN: 0167-6377
DOI: 10.1016/j.orl.2016.07.004
BibTeX: Download
Baes M., Oertel T., Weismantel R.:
Duality for mixed-integer convex minimization
In: Mathematical Programming 158 (2016), p. 547-564
ISSN: 0025-5610
DOI: 10.1007/s10107-015-0917-y
BibTeX: Download
Basu A., Oertel T.:
Centerpoints: A link between optimization and convex geometry
18th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2016 (Liege, BEL, 01.06.2016 - 03.06.2016)
In: Martin Skutella, Quentin Louveaux (ed.): Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 2016
DOI: 10.1007/978-3-319-33461-5_2
BibTeX: Download

2015

Adjiashvili D., Oertel T., Weismantel R.:
A polyhedral frobenius theorem with applications to integer optimization
In: SIAM Journal on Discrete Mathematics 29 (2015), p. 1287-1302
ISSN: 0895-4801
DOI: 10.1137/14M0973694
BibTeX: Download
Hildebrand R., Oertel T., Weismantel R.:
Note on the complexity of the mixed-integer hull of a polyhedron
In: Operations Research Letters 43 (2015), p. 279-282
ISSN: 0167-6377
DOI: 10.1016/j.orl.2015.03.002
BibTeX: Download

2014

Oertel T., Wagner C., Weismantel R.:
Integer convex minimization by mixed integer linear optimization
In: Operations Research Letters 42 (2014), p. 424-428
ISSN: 0167-6377
DOI: 10.1016/j.orl.2014.07.005
BibTeX: Download

2013

Baes M., Oertel T., Wagner C., Weismantel R.:
Mirror-descent methods in mixed-integer convex optimization
In: Michael Jünger, Gerhard Reinelt (ed.): Facets of Combinatorial Optimization, Berlin, Heidelberg: Springer-Verlag, 2013, p. 101-131
ISBN: 9783642381898
DOI: 10.1007/978-3-642-38189-8_5
BibTeX: Download