Ulf Friedrich

Postdoctoral researcher at the Technical University of Munich

After finishing my diploma in applied mathematics, I started working at Trier University as a research assistant (Wissenschaftlicher Mitarbeiter) in the Department of Mathematics and, after finishing my PhD in 2016, as a postdoc for the research training group Algorithmic Optimization funded by the German Science Foundation (DFG). Currently, I am employed as a postdoc at the Technical University of Munich.

Research

My research belongs to the broad field of discrete optimization and is a fusion of practical problem solving and theoretical abstraction. I am focusing on two projects at the moment: On the one hand, the application of MIP and MINLP techniques for the solution of practical problems from (survey) statistics and, on the other hand, the development of algorithms for IP that rely on techniques from complex analysis.

Map of Italy

Integer Optimization in Survey Statistics

The census conducted in Germany in 2011 was the major motivation to study stratified sampling problems. When a sample is drawn (for instance 10 percent of the population), it has to be distributed optimally among the population while respecting regional and structural constraints. Solving optimal allocation problems and their generalizations is important whenever a stratified sample is drawn. The map on the left illustrates an Italian business survey and is taken from a project with my colleagues Ralf Münnich and Martin Rupp.

Unit Disc

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 in my PhD thesis which relies on results from the field of analysis in several complex variables. Both fields seem to be unrelated at first sight and the appeal of the approach emerges from the surprising connections of pure mathematics and optimization theory. In particular, the path independence of complex integrals can be used to improve the numerical performance of the method, as depicted in the picture.

Publications

Work in Progress

  • Geometry of gross substitutes valuations, with S. de Vries and S. Raach, under review.
  • Optimal donor-limited nearest neighbor hot deck imputation based on a b-matching problem, with J. P. Burgard, S. de Vries and D. Kreber, under review.
  • Extended formulations for the stable set problem on wheels, with S. de Vries and B. Perscheid, under review.
  • Solving IP via complex integration, in preparation.
  • A computational study of hot deck imputation methods, with J. P. Burgard, D. Kreber and L. Kreber, in preparation.

PhD-Thesis

  • Discrete allocation in survey sampling and analytic algorithms for integer programming, Trier University, 2016. Examiners: Sven de Vries (Trier University) and Alexander Martin (FAU Erlangen-Nürnberg Unversity).

Activities

Upcoming Conference

I will give a talk at the ISMP 2018 in Bordeaux, France.

ALOP Summer School 2018

In August 2018, I will organize the next ALOP summer school on Mixed Integer Non-linear Progamming. Registration is open now!

FRICO 2017

We hosted the 21th Workshop on Future Research in Combinatorial Optimization (FRICO) in Trier in 2017.

Past Conferences and Talks

Recently, I have participated in the following international mathematical conferences:

  • SIGOPT Conference on Optmization 2018 in Kloster Irsee, Germany
    (talk “A path integral algorithm for IP with nonnegative input”)
  • Invited talk in the research seminar for optimization at the University of Augsburg
    (talk “Integer optimization for sample allocation and imputation”)
  • OR 2017 conference Berlin, Germany
    (talk “A network flow approach to address selection in populations”)
  • MIP 2017 Montreal, Canada
  • SIAM Conference on Optimization 2017 Vancouver, Canada
    (talk “Solving integer programming problems via numerical complex integration”)
  • SAMSI-WISO Workshop 2017 Duke University, Durham, NC
    (poster presentation “Discrete optimization in survey statistics”)
  • Workshop on Microsimulation 2016 Trier, Germany
    (talk “Optimal address allocation for microsimulation”)
  • COMPSTAT 2016 Oviedo, Spain
    (talk “Integer-valued algorithms for constrained optimal allocations in stratified sampling”)
  • EURO 2016 Poznan, Poland
    (talk “Discrete optimization of sample sizes in survey statistics”)
  • Arbeitskreis für mathematisch-statistische Methoden beim Statistischen Bundesamt 2016 Wiesbaden, Germany
    (talk “Allokationsverfahren zur Bestimmung ganzzahliger, optimaler Teilstichprobenumfänge”)
  • 2016 Mixed Integer Programming Workshop Miami, FL
    (poster “Solving integer programming problems with Cauchy’s theorem”)
  • SIGOPT 2016 Trier, Germany
    (talk “Fast algorithms for optimal sample sizes allocation”)

Contact Information