  Recently, data-enabled predictive control (DeePC) schemes based on Willems'
fundamental lemma have attracted considerable attention. At the core are
computations using Hankel-like matrices and their connection to the concept of
persistency of excitation. We propose an iterative solver for the underlying
data-driven optimal control problems resulting from linear discrete-time
systems. To this end, we apply factorizations based on the discrete Fourier
transform of the Hankel-like matrices, which enable fast and memory-efficient
computations. To take advantage of this factorization in an optimal control
solver and to reduce the effect of inherent bad conditioning of the Hankel-like
matrices, we propose an augmented Lagrangian lBFGS-method. We illustrate the
performance of our method by means of a numerical study.
