Software I’ve been working on (also check out my Github profile):

ProximalAlgorithms.jl. Efficient, generic Julia implementations of firstorder optimization algorithms for nonsmooth problems, based on operator splittings: forwardbackward splitting (proximal gradient method), DouglasRachford splitting (ADMM), Newtontype methods, primaldual splitting algorithms. Based on:

ProximalOperators.jl. Julia package to compute the proximal operator of several functions commonly used in nonsmooth optimization problems. Useful as building block to implement largescale optimization algorithms such as ADMM.

ForBES. MATLAB solver for nonsmooth optimization, contains a library of mathematical functions to formulate problems arising in control, machine learning, image and signal processing.

libLBFGS. C library providing the structures and routines to implement the limitedmemory BFGS algorithm (LBFGS) for largescale smooth unconstrained optimization. Contains a Mex interface to MATLAB.

libForBES. C++ framework for modeling and solving largescale nonsmooth optimization problems, will allow to interface many highlevel languages (including R, Python, Julia) to a unique solver capable of addressing nonsmooth optimization problems from several application fields.
Just for fun: