Optimization problems governed by partial differential equation (PDE) constraints arise in many important applications. Progress in computational and applied mathematics combined with the availability of rapidly increasing computer power steadily enlarges the range of applications that can be simulated numerically and for which optimization tasks, such as optimal design, parameter identification, and control are being considered. For most of these optimization problems, simple approaches combining off-the-shelf PDE solvers and optimization algorithms often lack robustness or can be very inefficient.
Successful solution approaches have to overcome challenges arising from the increasing complexity of applications and their mathematical models, the influence of the underlying infinite dimensional problem structure on optimization algorithms, and the interaction of PDE discretization and optimization.
This talk will combine a range of topics important to PDE constrained optimization, fusing techniques from a number of mathematical disciplines including optimal control, numerical optimization, numerical PDEs, linear algebra and numerical analysis and application specific structures.