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.