Students following the course should be able to recognise problems from the technical sciences that can be modelled as PDE constrained optimization problems. They should be able to formulate such problems in a mathematically satisfactory way, derive and prove properties of the models. Finally students should be able to approximate solutions to the problems using numerical algorithms. En studerende, der fuldt ud har opfyldt kursets mål, vil kunne:

• Recognise and formulate problems involving optimization with PDE constraints
• Understand and apply theory for optimization problems in Banach spaces
• Derive the adjoint PDE based on the Lagrangian formulation of PDE constraints
• Derive necessary optimitality conditions for PDE constrained problems
• Understand and apply gradient descent methods for the numerical solution of PDE constrained problems
• Understand and apply Newton methods for the numerical solution of PDE constrained problems
• Derive and understand the structure of saddle point systems related to PDE constrained optimization problems and apply suitable preconditioners
• Practice presentation and discussion of scientific material
• Reflect upon seminars delivered by leading experts in PDE constrained optimization

Basic Theory of Partial Differential Equations and Their Discretization; Theory of PDE-Constrained Optimization; Numerical Optimization Methods; Box-Constrained Problems; Nonsmooth PDE-Constrained Optimization; Saddle Point Systems; ODE-Constrained Optimization. 1. Numerical PDE-constrained optimization, Juan Carlos De los Reyes, Springer 2015 (available as ebook)

2. Optimal Control of PDEs, Fredi Tröltzsch, AMS, 2010. 25. april, 2016