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 an estimate of Clarke’s generalized
gradient of the objective function, obtained via calculation of the (approximate)
directional derivative along a certain set of directions. A search direction
is then calculated by applying a nonsmooth Newton-type approach. 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
