Solver-o-matic
"These days, even the most pure and abstract mathematics is in danger to be applied."
- Anonymous
Decision Tree for Nonsmooth Optimization Software
Your first choice should
be Quasi-Secant Method (QSM) for
nonsmooth possibly nonconvex minimization by A. Bagirov and
A. Ganjehlou. You can employ either analytically calculated
or approximated subgradients in your experiments (this can be
done automatically by selecting one parameter). The Fortran
77 source code of QSM is available for downloading.
If the function is highly nonlinear you may also try LMBM. Another option is SolvOpt, although theoretically SolvOpt is not supported for nonconvex functions.
