Ulf Friedrich

Dr. Ulf Friedrich

Otto von Guericke University Magdeburg, Germany

I joined the Institute of Mathematical Optimization at the Faculty of Mathematics of OVGU Magdeburg in 2021. I hold a permanent faculty position, which allows me to follow my own line of research and to teach independently. Beyond research and teaching, I participate in many of the faculty's outreach and recruitment activities.

My mathematical education started with studying applied mathematics at Trier University, where I also received my PhD in the Operations Research Group of Sven de Vries in 2016. As a postdoc, I joined the research training group Algorithmic Optimization in Trier. After that, I worked in the Operations Research Group of Andreas S. Schulz at the Technical University of Munich from 2018 to 2021.

Research

My research belongs to the broad field of mathematical optimization and is a fusion of practical problem solving and theoretical abstraction. At heart, I am a “MIP person”, mainly because I enjoy the broad range of applications and theoretical approaches that come with it. Here are some of the major topics I have been working on.

Regional decomposition of the household assignment problem

Integer Optimization in Applied Statistics

I study optimization problems arising in computational statistics, such as stratified sampling and, more recently, the geo-referencing step of spatial microsimulation models. Together with Lucas Moschen, Ralf Münnich, and Martin Schmidt, I have developed combinatorial methods for the resulting household assignment problem, in which households are matched to dwellings under regional distribution constraints. The picture is taken form our manuscript and illustrates the regional decomposition approach, which iteratively splits the region into smaller sub-regions.

Analytic Algorithms for IP

I study integer linear programming problems with the additional restriction that all input data has non-negative entries. For these problems, I have developed a novel solution approach which relies on results from the field of analysis in several complex variables. Both fields seem to be unrelated at first sight and the project connects pure mathematics and optimization theory in a beautiful way. In particular, the path independence of complex integrals can be used to improve the numerical performance of the method, as depicted in the picture. The research on the topic was supported by the Volkswagen Foundation Experiment! initiative in my project An Analytic Computational Solver for Integer Programming.

More Models and Methods in MIP

Besides these two topics, I work on a variety of models and methods in mixed-integer programming, such as partition problems, matchings, total unimodularity or extended formulations. Recently, I have also started to research the combinatorial structure of certain matrix cones.

Publications

Articles in Peer-Reviewed Journals

Computational Methods for the Household Assignment Problem, with Lucas Moschen, Ralf Münnich, and Martin Schmidt, accepted for publication in Mathematical Methods of Operations Research.
Recognizing Integrality of Weighted Rectangles Partitions, with Paul Deuker, Journal of Combinatorial Optimization, 49(19), 2025.
Computing optimized path integrals for knapsack feasibility, with Endric Daues, INFORMS Journal on Computing, 34(4):2163–2176, 2022.
Geometry of gross substitutes valuations, with S. de Vries and S. Raach, Discrete Applied Mathematics 272:16-23, 2020.
An extended formulation for the 1‐wheel inequalities of the stable set polytope, with S. de Vries and B. Perscheid, Networks 75(1):86-94, 2020.
Multivariate optimal allocation with box-constraints, with R. Münnich and M. Rupp, Austrian Journal of Statistics 47(2):33-52, 2018.
Fast integer-valued algorithms for optimal allocations under constraints in stratified sampling, with R. Münnich, S. de Vries and M. Wagner, Computational Statistics and Data Analysis 92:1-12, 2015.

More publications

Solving IP via complex integration on shortest paths.
On the relation between intersection pattern matrices, {0,1}-cp matrices, and Bernoulli matrices, with Ralf Werner.
Projective cutting planes for general QP with indicator constraints, with Dennis Kreber.

PhD Thesis

Discrete allocation in survey sampling and analytic algorithms for integer programming, Dr. rer. nat, Trier University. Reviewers: Sven de Vries and Alexander Martin

Diploma Thesis

On the local regularity of partial differential equations, Dipl.-Math., Trier University.

Activities

MathemaTHEK

In 2026, the MathemaTHEK presents the many aspects of mathematics in the Magdeburg City Library.

Recent Conferences and Talks

Recently, I have presented my research at the following scientific events:

27th Combinatorial Optimization Workshop in Aussois, France
(talk “Recognizing integrality of weighted rectangles partitions”)
Small Area Estimation Survey and Data Science 2023-24 in Lima, Peru
(talk “On the interplay of microsimulation and mathematical optimization”)
9th World Congress of the International Microsimulation Associtation in Vienna, Austria
(talk “Improving the household-dwelling allocation in a dynamic microsimulation model”)
OR 2023 in Hamburg, Germany
(talk “Fair and stable school districting”)
25th Combinatorial Optimization Workshop in Aussois, France
(lightning talk “Characterizing {0,1}-cp matrices and bounds on the {0,1}-cp rank”)
Research seminar for optimization at the University of Augsburg, Germany
(talk “Characterization of 0-1-cp matrices and bounds on the 0-1-cp rank”)
Forum Experiment! 2021, Hannover, Germany
(talk “An analytic computational solver for integer programming”)

Contact Information

Otto von Guericke University, Faculty of Mathematics, Universitätsplatz 2, 39106 Magdeburg, Germany
+49 391 67 52155
ulf.friedrich@ovgu.de (office) or friedrich@optmath.de