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Numerical Mathematics and Optimization

Academic staff

Dr. Eike Börgens

Research Interests

  • Optimization
  • Alternating Direction Methods of Multipliers (ADMM)
  • Nash Problems
  • Generalized Nash Problems
  • Splitting Methods for (generalized) Nash Problems

  • Eike Börgens
    ADMM-Type Methods for Optimization and Generalized Nash Equilibrium Problems in Hilbert Spaces
    Dissertation, November 2020 (Preprint)
     
  • Eike Börgens, Christian Kanzow, Patrick Mehlitz and Gerd Wachsmuth
    New Constraint Qualifications for Optimization Problems in Banach Spaces Based on Asymptotic KKT Conditions
    SIAM Journal on Control and Optimization 30 (4), 2020, pp. 2956 - 2982 (DOI: 10.1137/19M1306804) (Preprint)
     
  • Eike Börgens and Christian Kanzow
    ADMM-type Methods for Generalized Nash Equilibrium Problems in Hilbert Spaces
    SIAM Journal on Optimization (Preprint), to appear
     
  • Eike Börgens, Christian Kanzow and Daniel Steck
    Local and Global Analysis of Multiplier Methods for Constrained Optimization in Banach Spaces.
    SIAM Journal on Control and Optimization 57 (6), 2019, pp. 3694 - 3722 (DOI: 10.1137/19M1240186) (Preprint) ( BibTeX )
     
  • Eike Börgens and Christian Kanzow
    A Distributed Regularized Jacobi-type ADMM-Method for Generalized Nash Equilibrium Problems in Hilbert Spaces.
    Numerical Functional Analysis and Optimization 39 (12), pp. 1316 - 1349 (DOI: 10.1080/01630563.2018.1477800) (Preprint not available since it is identical to the accepted version) ( BibTeX )
     
  • Eike Börgens and Christian Kanzow
    Regularized Jacobi-type ADMM-Methods for a Class of Separable Convex Optimization Problems in Hilbert Spaces
    Computational Optimization and Applications 73(3), pp. 755 - 790 (DOI:  10.1007/s10589-019-00087-9) (Preprint) ( BibTeX )

Winter Term 2020/2021

  • Tutorial in Analysis 1 (in collaboration with Prof. Dr. Jörn Steuding and Tobias Geiger)
     

­­Summer Term 2020

  • Tutorial in Linear Algebra 2 (in collaboration with Prof. Dr. Daniel Wachsmuth, Marvin Dippel and Tobias Geiger)
     

Winter Term 2019/2020

  • Tutorial in Operations Research (in collaboration with Prof. Dr. Daniel Wachsmuth)
     

Summer Term 2019

  • Supplementary lesson in Mathematics for computer science students (in collaboration with Prof. Dr. Manfred Dobrowolski, Andreas Raharja and Simon Reinwand)
     

Winter Term 2018/2019

  • Tutorial in Analysis 1 (in collaboration with PD. Dr. Jürgen Grahl, Tim Breitenbach and Melina Kienle)
     

Summer Term 2018

  • Tutorial in Numerical Analysis 2 (in collaboration with Prof. Dr. Manfred Dobrowolski)
     

Winter Term 2017/2018

  • Tutorial in Numerical Analysis 2 (in collaboration with Prof. Dr. Manfred Dobrowolski)
     

Summer Term 2017

  • Tutorial in Operations Research (in collaboration with Prof. Dr. Christian Kanzow)