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
It does not really matter. All the solvers recommended for your
problem can handle both convex and nonconvex problems.
Your first choice should be Limited Memory
Bundle Method (LMBM) (you need to code difference
approximations by yourself).
LMBM is specifically developed for
large-scale nonsmooth optimization by N. Karmitsa. It works best
for highly nonlinear functions.
The Fortran 77 source code and the
mex-driver (for MatLab users) are available.
For other choices, see e.g.
