The term ’PDE-constrained optimization’ refers to optimization problems which involve partial differential equations as side constraints. Problems of this class arise, for instance, in parameter identiﬁcation as well as optimal control. Dealing with them appropriately and efﬁciently touches upon a wide range of topics, such as optimization theory in function spaces, taylored discretizations, error estimation, and numerical linear algebra. In this presentation we focus on some of the properties of linear systems arising as optimality conditions for discretized optimal control problems. Particular attention will be given to problems with additional inequality constraints, which exhibit some unexpected features.
Chemnitz University of Technology, Germany