Multiple shooting and balanced error estimation for parabolic optimal control problems with additional constraints



In this work, we investigate several aspects of multiple shooting methods in the context of parabolic optimal control problems. For ODE and DAE optimal control problems, shooting methods have been developed and widely and successfully applied during the past three decades. However, their application to PDE constrained optimal control is a rather new topic of research where lots of questions still remain open despite some promising approaches in the last five years. The aims of this project are:
  1. to develop algorithms for both indirect and direct multiple shooting in the PDE optimal control context, thereby testing several possible concrete realizations,
  2. to implement these algorithms efficiently,
  3. to clarify relations between multiple shooting and similar classes of methods (e.g. parareal methods),
  4. to develop and apply an a posteriori error estimator for the multiple shooting approaches which is based on the dual weighted residual (DWR) method and capable of balancing the contributions of discretization and iteration errors,
  5. to include optimal control problems with additional control and state constraints in the multiple shooting framework for PDE optimal control,
  6. to apply the developed methods to problems from image processing.
 
This project is part of the DFG priority program 1253.