This project is concerned with the development, analysis and application of new, innovative mathematical techniques for the solution of constrained optimization problems where a partial differential equation (PDE) or a system of PDEs appears as an essential part of the constraints. Such optimization problems arise in a wide variety of important applications in the form of, e.g., parameter identification problems, optimal design problems, or optimal control problems. The efficient and robust solution of PDE constrained optimization problems has a strong impact on more traditional applications in, e.g., automotive and aerospace industries and chemical processing, as well as on applications in recently emerging technologies in materials and life sciences including environmental protection, bioand nanotechnology, pharmacology, and medicine. The appropriate mathematical treatment of PDE constrained optimization problems requires the integrated use of advanced methodologies from the theory of optimization and optimal control in a functional analytic setting, the theory of PDEs as well as the development and implementation of powerful algorithmic tools from numerical mathematics and scientific computing. Experience has clearly shown that the design of efficient and reliable numerical solution methods requires a fundamental understanding of the subtle interplay between optimization in function spaces and numerical discretization techniques which can only be achieved by a close cooperation between researchers from the above mentioned fields.