Trends in PDE Constrained Optimization

Optimization problems subject to constraints governed by partial differential equations (PDEs) are among the most challenging problems in the context of industrial, economical and medical applications. Almost the entire range of problems in this field of research was studied and further explored within the framework of the priority program 1253 on "Optimization with Partial Differential Equations" of the Deutsche Forschungsgemeinschaft (DFG) during the period from 2006 to 2013. The investigations were driven by fascinating future applications and challenging mathematical problems that arise in the field of PDE constrained optimization. New analytic and algorithmic paradigms have been developed, implemented and validated in the context of real-world applications. In this special volume contributor from more than fifteen German universities combines the results of this interdisciplinary program with a focus on applied mathematics. The book is structured in five sections on "Constrained Optimization, Identification and Control", "Shape and Topology Optimization", "Adaptivity and Model Reduction", "Discretization: Concepts and Analysis" and "Applications". Peer-reviewed research articles present the most recent results in the field of PDE constrained optimization and control problems. Informative survey articles give an overview over topics that set sustainable trends for future research. This special volume is, therefore, not only interesting for mathematicians but also for engineers and for natural and medical scientists who are working on processes that can be modeled by PDEs.