Michael Hintermueller

A PDE-Constrained Generalized Nash Equilibrium Approach for Modeling Gas Markets with Transport

  • Veronika Grimm
  • Michael Hintermueller
  • Olivier Huber
  • Lars Schewe
  • Martin Schmidt
  • Gregor Zöttl
    • Categories Game Theory, Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    We investigate a class of generalized Nash equilibrium problems (GNEPs) in which the objectives of the individuals are interdependent and the shared constraint consists of a system of partial differential equations. This setup is motivated by the modeling of strategic interactions of competing firms, which explicitly take into account the dynamics of transporting a commodity, … Read more

    Optimization with learning-informed differential equation constraints and its applications

  • Guozhi Dong
  • Michael Hintermueller
  • Kostas Papafitsoros
    • Categories Biomedical Applications, Infinite Dimensional Optimization, Nonlinear Optimization

    Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through data-driven techniques are studied. A particular focus is on the analysis and on numerical methods for problems with machine-learned components. For a rather general context, an error analysis … Read more