This paper has two main objectives. Firstly, the performance of a recently developed Nonlinear programming algorithm based on Augmented Lagrangians on a family of optimization problems related to the classical Kissing Problem is reported. The test problems are easily defined in purely mathematical terms and its reproduction using standard scientific languages does nor seem to be prone to human errors. Therefore, the figures presented here can be useful to developers of other optimization algorithms. Secondly, the practical results on the geometrical problems described in this paper have an independent interest from a large variety of perspectives, including the historical one. In particular, there exist a large number of related open mathematical problems, and the ability of dealing with them numerically should help to their rigorous elucidation.7017586