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?