NonSmooth Optimization (NSO) Software
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NSO Software available here
General Nonsmooth Optimization
LMBM 
Limited memory bundle method for largescale nonsmooth, possibly nonconvex optimization by N. Karmitsa (Fortran 77 and mexdriver for MatLab users). See LDGB for Fortran 95 version of LMBM. 
DBundle 
Diagonal bundle solver for
general, possible nonconvex, largescale nonsmooth minimization by N. Karmitsa
(Fortran 95). 
MPBNGC 
Proximal bundle method for nonsmooth possibly nonconvex (multiobjective) minimization by M.M. Mäkelä (Fortran 77). The code includes the constraint handling (bound constraints, linear constraints, and nonlinear/nonsmooth constraints). MPBNGC can also be used (free for academic purposes) via WWWNIMBUS system.

QSM 
Quasisecant solver for nonsmooth possibly nonconvex minimization
by A. Bagirov and A. Ganjehlou (Fortran 77). The user can employ either
analytically calculated or approximated subgradients in his experiments
(this can be done automatically by selecting one parameter). 
SMDB 
Splitting metrics diagonal bundle solver for
general, possible nonconvex, largescale nonsmooth minimization by N. Karmitsa
(Fortran 95). 
Derivative Free Optimization
LDGB 
Limited memory discrete gradient bundle solver for derivative free
general, possible nonconvex, nonsmooth minimization by N. Karmitsa
(Fortran 95).
To apply LDGB, one only needs to compute at every point the value
of the objective function. The subgradient will be approximated.
You can also use this code as Fortran 95 version of LMBM
(due to some implementational facts it might use less subgradient evaluations
than the previous version). 
DDGBundle 
Diagonal discrete gradient bundle solver for derivative free
general, possible nonconvex, nonsmooth minimization by N. Karmitsa
(Fortran 95).
To apply DDGBundle, one only needs to compute at every point the value
of the objective function. The subgradient will be approximated.

DGM 
Discrete gradient solver for derivative free optimization by
A. Bagirov, B. Karasozen and M. Sezer (Fortran 77).
To apply DGM, one only needs to compute at every point the value
of the objective function. The subgradient will be approximated. 
QSM 
Quasisecant solver with discrete gradients. See QSM above. 
DC Programming
DBDC 
Proximal double bundle solver for nonsmooth DC programming (difference of two convex functions) by K. Joki (Fortran 95). 
PBDC 
Proximal bundle solver for nonsmooth DC programming by K. Joki (Fortran 95). 
NonsmoothDCA 
Solver for nonsmooth DC programming by A. Bagirov (Fortran 77). The solver is an implemantation of wellknown DCA algorithm by Le Thi Hoai An and Pham Dinh Tao. 
TCM 
Truncated codifferential solver for nonsmooth DC programming by A. Bagirov (Fortran 77). 
Multiobjective Nonsmooth Optimization
MPBNGC 
Multiobjective proximal bundle solver. See MPBNGC above.

MDBDC 
Multiobjective double bundle method for nonsmooth DC programming by K. Joki and O. Montonen (Fortran 95). MDBDC is able to handle problems which objective and constraint functions can be presented as a difference of two convex (DC) functions. 
Links to some other NSO solvers and softwares

Proximal bundle method for nonsmooth DC programming Matlab implementations of solvers for nonsmooth DC programming by W. de Oliveira.

MinNS Solver for nonsmooth (possibly)
constrained problems by S. Bochkanov. The solver is part of nonlinear
optimization suite in ALGLIB (numerical analysis library).
It uses internally the gradient sampling algorithm (C++/C#).

OSGA MatLab package for solving
largescale structured convex optimization
by M. Ahookhosh.

SolvOpt Solver for local nonlinear optimization
problems is an implementation of Shor's ralgorithm by A. Kuntsevich
and F. Kappel. The constraints may be taken into
account by the method of exact penalization (MatLab, C and Fortran).

GANSO Programming library for Global And
NonSmooth Optimization by CIAO (C/C++).

GradSamp Gradient sampling solver by
J. Burke, A. Lewis, and M. Overton (MatLab).

HANSO Hybrid Algorithm for NonSmooth
Optimization by
J. Burke, A. Lewis, and M. Overton (MatLab).

OBOE Oracle Based Optimization Engine for
convex minimization by J.P. Vial and N. Sawhney
(C++).

PNEW BundleNewton method for unconstrained and linearly constrained
NSO by L. Luksan and J. Vlcek (Fortran 77).

PVAR Variable metric bundle method for unconstrained and linearly
constrained NSO by L. Luksan and J. Vlcek (Fortran 77).

PBUN
Proximal bundle method for unconstrained and linearly
constrained NSO by L. Luksan and J. Vlcek (Fortran 77).

PMIN solver for MinMaxproblems by L. Luksan
(Fortran 77).
Nonsmooth Test Problems
Solveromatic
Solveromatic is an online
decision tree for choosing a NSO solver.
Solveromatic will tell you which method/solver is the most suitable
for solving your problem.