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 as a faculty member in 2021. 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. Currently, I am working in two major areas: On the one hand, the application of MIP and MINLP techniques for the solution of application problems from data science or computational statistics and, on the other hand, the development of algorithms for IP that rely on techniques from complex analysis in several variables.

Integer Optimization in Applied Statistics

The census conducted in Germany in 2011 was the major motivation to study computational statistics and, for example, stratified sampling problems. Here, a sample is drawn (for instance 10 percent of the population) which has to be distributed among the population in such a way that the overall variance is minimized and certain structural and legal constraints are respected. Solving optimal allocation problems and their generalizations is important in many data-driven applications. The map on the left illustrates an Italian business survey and is taken from a project with my colleagues Ralf Münnich and Martin Rupp.

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. This research is part of my project An Analytic Computational Solver for Integer Programming funded by the Volkswagen Foundation in their Experiment! initiative.

Publications

Articles in Peer-Reviewed Journals

Recognizing Integrality of Weighted Rectangles Partitions, with Paul Deuker, Journal of Combinatorial Optimization, to appear.
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

Computational Methods for the Household Assignment Problem, with Lucas Moschen, Ralf Münnich, and Martin Schmidt.
Projective cutting planes for general QP with indicator constraints, with Dennis Kreber.
Solving IP via complex integration on shortest paths.
Geo-referencing of households as mathematical optimization problem, with Ralf Münnich and Kendra Reiter.
On the relation between intersection pattern matrices, {0,1}-cp matrices, and Bernoulli matrices, with Ralf Werner.

PhD Thesis

Discrete allocation in survey sampling and analytic algorithms for integer programming, Trier University, 2016. Reviewers: Sven de Vries and Alexander Martin.

Activities

Recent Conferences and Talks

In the last three years, I have presented my work at the following occasions:

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”)
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”)

Research training group MathCoRe

I am an associated member of the DFG research traning group Mathematical Complexity Reduction (MathCoRe) at OVGU.

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