Solver-o-matic
Decision Tree for Nonsmooth Optimization Software
It does not really matter. Both the solvers suitable for your
problem use relatively small amount of iterations.
Your first choice should be Limited Memory
Bundle Method (LMBM) by N. Karmitsa. LMBM is specifically developed for
large-scale nonsmooth optimization but, naturally,
it can be used also for smaller problems. It works best
for highly nonlinear functions.
The Fortran 77 source code and the
mex-driver (for MatLab users) are available.
Not satisfied?