Solver-o-matic
Decision Tree for Nonsmooth Optimization Software
Your first choice should
be Discrete Gradient Method (DGM)
for derivative free optimization by A. Bagirov, B. Karasozen
and M. Sezer. To apply DGM, you only need to compute at
every point the value of the objective function. The
subgradient will be approximated. The Fortran 77 source code
of DGM is available for downloading.
Not satisfied?