Research interests

Optimization

  • Shape optimization problems and their numerical treatment / optimization methods in shape spaces
  • Analytical and numerical treatment of constrained optimization problems (in particular, constraints in form of partial differential equations and variational inequalities)
  • Stochastic approximation / optimization under uncertainties
  • Modelling of optimization problems

 

Shape spaces and their structures

  • Riemannian manifolds
  • Shape spaces as diffeological spaces