On time optimal control of the wave equation and its numerical realization as parametric optimization problem

摘要

Time optimal control of the wave equation is analyzed on the basis of a regularized formulation which is considered as a bilevel optimization problem. For the lower level problems, which are constrained optimal control problems for the wave equation, a detailed sensitivity analysis is carried out. Further a semismooth Newton method is analyzed and proved to converge locally superlinearly. Numerical examples are provided.