Solver-o-matic

Your first choice should be Quasi-Secant Method (QSM) with discrete gradients 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.

• Try LMBM with difference approximations.
• Try SolvOpt with difference approximations.