On Convergence of Binary Trust-Region Steepest Descent

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.