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 Proximal
Bundle Method (MPBNGC) by M.M. Mäkelä.
The code includes the constraint handling (bound constraints,
linear constraints, and nonlinear/nonsmooth constraints). MPBNGC
can also be used
via
WWW-NIMBUS -system.
Not satisfied?