511 RWTH Publication No: 814243        2021        IGPM511.pdf
TITLE State Elimination for Mixed-Integer Optimal Control of PDEs by Semigroup Theory
AUTHORS Sven Leyffer, Sebastian Sager, Anna Thünen
ABSTRACT Mixed-integer optimal control problems governed by PDEs (MIPDECO) are powerful modeling tools but also very challenging in terms of theory and computation. We propose a highly efficient state elimination approach for MIPDECOs that are governed by PDEs that have the structure of an abstract ODE in function space. This allows us to avoid repeated calculations of the states for all time steps and our approach is applied only once before starting the optimization. The presentation of theoretical results are complemented by numerical experiments.
KEYWORDS mixed-integer nonlinear programming, parabolic PDE, optimal control