  In this chapter, we are concerned with inverse optimal control problems,
i.e., optimization models which are used to identify parameters in optimal
control problems from given measurements. Here, we focus on linear-quadratic
optimal control problems with control constraints where the reference control
plays the role of the parameter and has to be reconstructed. First, it is shown
that pointwise M-stationarity, associated with the reformulation of the
hierarchical model as a so-called mathematical problem with complementarity
constraints (MPCC) in function spaces, provides a necessary optimality
condition under some additional assumptions on the data. Second, we review two
recently developed algorithms (an augmented Lagrangian method and a nonsmooth
Newton method) for the computational identification of M-stationary points of
finite-dimensional MPCCs. Finally, a numerical comparison of these methods,
based on instances of the appropriately discretized inverse optimal control
problem of our interest, is provided.
