  In this paper we consider bound-constrained mixed-integer optimization
problems where the objective function is differentiable w.r.t.\ the continuous
variables for every configuration of the integer variables. We mainly suggest
to exploit derivative information when possible in these scenarios: concretely,
we propose an algorithmic framework that carries out local optimization steps,
alternating searches along gradient-based and primitive directions. The
algorithm is shown to match the convergence properties of a derivative-free
counterpart. Most importantly, the results of thorough computational
experiments show that the proposed method clearly outperforms not only the
derivative-free approach but also a state-of-the-art solver both in terms of
efficiency and effectiveness.
