  In this paper we propose an heuristic to improve the performances of the
recently proposed derivative-free method for nonsmooth optimization CS-DFN. The
heuristic is based on a clustering-type technique to compute a direction {
which relies on an estimate of Clarke's generalized gradient} of the objective
function. As such, this direction (as it is shown by the numerical experiments)
is a good descent direction for the objective function. We report some
numerical results and comparison with the original CS-DFN method to show the
utility of the proposed improvement on a set of well-known test problems.
