Solver-o-matic
Decision Tree for Nonsmooth Optimization Software
It doesn't really matter. Quasi-Secant Method (QSM) with discrete gradients can solve both. QSM is a quasi-secant solver 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.
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