Solver-o-matic
Decision Tree for Nonsmooth Optimization Software
Not a problem. 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.
For other choices, see e.g.