  Binary trust-region steepest descent (BTR) and combinatorial integral
approximation (CIA) are two recently investigated approaches for the solution
of optimization problems with distributed binary-/discrete-valued variables
(control functions). We show improved convergence results for BTR by imposing a
compactness assumption that is similar to the convergence theory of CIA. As a
corollary we conclude that BTR also constitutes a descent algorithm on the
continuous relaxation and its iterates converge weakly-$^*$ to stationary
points of the latter. We provide computational results that validate our
findings. In addition, we observe a regularizing effect of BTR, which we
explore by means of a hybridization of CIA and BTR.
