Dissertationen

Promotionsarbeiten

Promotionsthemen behandeln in der Regel komplexe mathematische Optimierungsprobleme, für die es bislang keine zufriedenstellenden Lösungsmethoden oder theoretischen Grundlagen gibt. Die Aufgabenstellungen resultieren häufig aus konkreten ingenieur- und naturwissenschaftlichen Fragestellungen oder aus Anwendungen in Industrie und Wirtschaft, können sich aber auch mit der Theorie gewisser Klassen von Optimierungsproblemen beschäftigen. Dabei interessiert sich unsere Arbeitsgruppe besonders für solche Optimierungsprobleme, bei denen partielle Differentialgleichungen als Nebenbedingungen auftreten. Dies ist z.B. bei der Optimierung von Strömungsprozessen und mechanischen Strukturen der Fall. Zudem werden in der Arbeitsgruppe neuartige Verfahren für nichtlineare und gemischt-ganzzahlige nichtlineare Optimierungsprobleme entwickelt.

Aktuelle Promotionsarbeiten

  • Robust shape optimization of electromechanical energy converters
    Björn Polenz (Prof. Ulbrich)
  • Simulation Based Optimization and Optimal Design of Experiments for Wetting Processes
    Elisabeth Diehl (Prof. Ulbrich)
  • Adaptive Multigrid Methods for Fluid-Structure Interaction Optimization
    Sarah Essert (Prof. Ulbrich)
  • Eigenvalue Optimization with respect to Shape-Variations in Electro-Magnetic Systems
    Christine Herter (Prof. Wollner)
  • Model-guided Machine Learning
    Isabel Jacob (Prof. Ulbrich)
  • Detecting and handling of model uncertainty in the context of robust PDE constrained optimization
    Alexander Matei (Prof. Ulbrich)
  • Discretisation Methods for Incompressible Fractures
    Seshadri Reddy Basava (Prof. Wollner)
  • Mixed-Integer Nonlinear Optimization of Heating Networks
    Lea Rehlich (Prof. Ulbrich und Prof. Pfetsch)
  • Numerical approximation of optimal control problems for hyperbolic conservation laws
    Paloma Schäfer Aguilar (Prof. Ulbrich)
  • Optimal control of scalar transport in incompressible fluid flow
    Cedric Sehrt (Prof. Ulbrich)
  • Optimal Control and Generalized Nash Equilibrium Problems on Networks of Scalar Conservation Laws
    Marcel Steinhardt (Prof. Ulbrich)
  • Optimal control in the coefficients of variational inequalities
    Nicolai Simon (Prof. Wollner)
  • Mixed-integer nonlinear optimization methods for the robust optimization of renewable energy systems based on iron
    Elisa Corbean (Prof. Ulbrich)

Abgeschlossene Promotionsarbeiten

  • Optimization of Energy Systems for Settlements Involving Renewable Energies
    Kristina Janzen (Prof. Ulbrich)
  • Solution of Nonconvex/Nonsmooth Nash Games: Optimality Conditions and Algorithms
    Daniel Nowak (Prof. Schwartz)
  • Optimization methods for mathematical programs with equilibrium constraints in function spaces based on adaptive error control and reduced order approximations
    Anne-Therese Rauls (Prof. Ulbrich)
  • Multilevel Optimization based on Reduced Order Models with Application to Fluid-Structure Interaction
    Johanna Biehl (Prof. Ulbrich)
  • Multi-Leader-Follower Games in Function Space
    Jan Becker (Prof. Schwartz)
  • Simulation-based optimization methods for the deep drawing of branched structures
    Anna Walter (Prof. Ulbrich)
  • Shape Optimization for Frictional Contact Problems by a Bundle Trust-Region Method for Constrained Nonsmooth Problems
    Benjamin Horn (Prof. Ulbrich)
  • Shape Optimization with the Navier-Stokes and Boussinesq equations in the infinite and discrete case
    Michael Fischer (Prof. Ulbrich)
  • Analysis and Optimal Control of quasilinear parabolic equations in divergence form
    Hannes Meinlschmidt (Prof. Ulbrich)
  • Numerical analysis of parabolic optimal control problems with restrictions on the state and its first derivative
    Francesco Ludovici (Prof. Wollner)
  • Multilevel Methods for PDE-constrained Optimization with State Constraints
    Stefanie Bott (Prof. Ulbrich)
  • Simulation-based optimization methods for the deep drawing of branched structures
    Daniela Koller (Prof. Ulbrich)
  • Optimal Control of Switched Networks for Nonlinear Hyperbolic Conservation Laws
    Sebastian Pfaff (Prof. Ulbrich)
  • Mixed Integer Nonlinear Models in Wireless Networks
    Anne Philipp (Prof. Ulbrich)
  • Optimal Design and Control of Adaptronic Systems
    Carsten Schäfer (Prof. Ulbrich)
  • Optimal Flow Control based on POD and MPC and an Application to the Cancellation of Tollmien-Schlichting Waves
    Jane Ghiglieri (Prof. Ulbrich)
  • Geometry Optimization of Branched Sheet Metal Structures with a Globalization Strategy by Adaptive Cubic Regularization
    Thea Göllner (Prof. Ulbrich)
  • Robust optimization of active trusses via Mixed-Integer Semidefinite Programming
    Kai Habermehl (Prof. Ulbrich)
  • Robust Nonlinear Programming with Discretized PDE Constraints using Second-order Approximations
    Adrian Sichau (Prof. Ulbrich)
  • Multilevel Optimization of Turbulent Flows by Discrete Adjoint Techniques
    Rolf Roth (Prof. Ulbrich)
  • Adjoint-Based Adaptive Multilevel Shape Optimization based on Goal-Oriented Error Estimators for the Instationary Navier-Stokes Equations
    Christian Brandenburg (Prof. Ulbrich)
  • Conditional Value-at-Risk Optimization for Credit Risk Using Asset Value Models
    Matthias Heidrich (Prof. Ulbrich)
  • Geometry Optimization with PDE Constraints and Applications to the Design of Branched Sheet Metal Products
    Wolfgang Hess (Prof. Ulbrich)
  • Adaptive Multilevel SQP-Methods for PDE-constrained Optimization
    Jan Carsten Ziems (Prof. Ulbrich)
  • Mixed Integer Second Order Cone Programming
    Sarah Drewes (Prof. Ulbrich)
  • Copositive Matrices, Copositive Programming, and Applications
    Stefan Bundfuss (Prof. Miriam Dür)
  • Formoptimierung mit Variationsungleichungen als Nebenbedingung und eine Anwendung in der Kieferchirurgie
    Jan Christoph Wehrstedt (Prof. Ulbrich mit Martin Brokate)
  • Über die Homogenisierung von Netzwerk-Differentialgleichungen
    Erik Kropat (Prof. Ulbrich mit Günter Leugering)