Mirko Hahn

Combinatorial Integral Approximation for Mixed-Integer PDE-Constrained Optimization Problems

  • Mirko Hahn
  • Sebastian Sager
    • Categories (Mixed) Integer Nonlinear Programming, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization Tags , , ,

    We apply the basic principles underlying combinatorial integral approximation methods for mixed-integer optimal control with ordinary differential equations in general, and the sum-up rounding algorithm specifically, to optimization problems with partial differential equation (PDE) constraints. By doing so, we identify two possible generalizations that are applicable to problems involving PDE constraints with mesh-dependent integer variables, … Read more

    Mixed-Integer PDE-Constrained Optimal Control of Gas Networks

  • Mirko Hahn
  • Sven Leyffer
  • Victor M. Zavala
    • Categories (Mixed) Integer Nonlinear Programming, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization Tags , , ,

    We develop a mixed-integer optimal control model with partial differential equation (PDE) constraints for gas transport networks, designed for controlling extreme state transitions, such as flow reversals. Our model shows how to combine binary compressor controls with PDE flow models. We model the flow of gas using a variant of the Euler equations, which we … Read more