Summary
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, bio- and 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.
Having this in mind, the proposed project has two equally important goals. The first one is the creation of a network of leading European and US research teams in the area of PDE constrained optimization and its applications to provide an improved theoretical understanding of the basic principles and to develop, analyze and implement efficient and reliable numerical solution techniques. The second one is to make these tools accessible to those industries where there is an increasing need for advanced optimization methods that lead to a significantly better operational behavior of existing devices and systems as well as to the development of new, innovative products. Herewith, the project participants would like to give a valuable contribution to the scientific progress, the improvement of industrial processes, the welfare and development of the nations and to the education of its people. Indeed, this project will reveal a carefully prepared communication among its participants from the academic world and with the various practitioners from outside of the universities, continuous education with a variety of teaching and training programs, workshops and conferences, scientific publications in premium journals and reports to interested parts of the publicity as well as the active integration and exchange of advanced students.
Programme proposal
More information can be found in the Programme brochure
Keywords
Optimization and optimal control, partial differential equations, numerical analysis, scientific computing
Duration
5 years from October 2008 until October 2013
