Scoring and numerical optimization of protein-ligand poses is an integral part of docking tools. Although many scoring functions exist, many of them are not continuously differentiable and they are rarely explicitly analyzed with respect to their numerical optimization behavior. Here, we present a consistent scheme for pose scoring and gradient-based pose optimization. It consists of a novel variant of the BFGS algorithm enabling step-length control, named LSL-BFGS (limited step length BFGS), and the empirical JAMDA scoring function designed for pose prediction and good numerical optimizability. The JAMDA scoring function shows a high pose prediction performance in the CASF-2016 docking power benchmark, top-ranking a pose with an RMSD of ≤2 Å in about 89% of the cases. The combination of JAMDA scoring with the LSL-BFGS algorithm shows a significantly higher optimization locality (i.e., no excessive movement of poses) than with the classical BFGS algorithm while retaining the characteristically low number of scoring function evaluations. The JAMDA scoring and optimization scheme is freely available for noncommercial use and academic research.