Software
One of 640 (as of May 2020) Mathworks contributors to have a submission with 25 five star ratings “5Star Galaxy Level 5”.
Github software
Most of our group’s latest software is on github. These are github project or user pages for students who have been in our research group or collaborated with our group:
 Stephen and cvx/tfocs projects (paper)
 James: safe NonNeg. Least Squares (paper)
 Farhad: RandomizedClusteredNystrom
 Eric: SparseKMeans (paper)
 Osman
 Angran
 Ibrohim
 Noki:
 Claudia
 TzuChi
 Kevin
 Jacob S: optimal_ultrasound_encoding (paper)
 Liam:
 Jaden
 Jacob T: Capstone project on deep learning for genomic data
 Will Shand: LSHFunctions.jl
 Akshay: minimaxfidelityestimation (paper)
 Gregor
 Erik
 Richie
 Lucas
 Richard: SL REML (paper)
 Marc: MDSpectralAnalysis
 Jeff: Hadamard Transform
A few specific software packages

Misc Python optimization routines for classic first and second order methods, as part of the optimization class I teach. I think there may be a bug in the one of the linesearch options, but otherwise it should work well.

Random sketching operators in Matlab and Python, as part of the class I teach. This has Gaussian sketch, Fast Johnson Lindenstrauss (with FFT or a fast Hadamard), and count sketch. The Hadamard and count sketch have C functions to make them extra fast. (For the tensor product sketches, which is more complicated, see Osman’s github page ).

Exact linesearch for LASSO
Simple Matlab code for exact stepsize selection for LASSO objectives, and Exact linesearch for LASSO Tech. Report which describes the method. 
Sparsified KMeans faster Kmeans for big data (2015)
Uses fast JohnsonLindenstrauss ideas to appropriately sample from big datasets. This is a onepass algorithm that performs Kmeans clustering, suitable for distributed datasets. It also works on incore problems and is much faster than Matlab’s default Kmeans, and uses modern ideas on initialization. Hosted in github, BSD license. A version for GMM, written in Python and C, is also available. 
LBFGSBC C version of LBFGSB (2015)
A version of LBFGSB 3.0 in C, with Matlab mex wrapper. Hosted on github, BSD license. 
fastRPCA fast robust PCA (2014)
A Matlab software package to solve all variants of robust PCA and stable principal component pursuit (SPCP) problems. This is actively maintained, and hosted on github under the BSD license. Derek Driggs has forked this to make an improved fastRPCA that uses the tricks from our RPCA marginalization paper.

zeroSR1 zero SR1 (2013)
A Matlab software package that is the only rigorous quasiNewton method to solve the nonsmooth LASSO problem. We use new results from convex analysis to show that a quasiNewton update can be done in closedform on a proximal objective. Existing approaches would solve the update via a slow iterative method, or smooth the problem, or apply quasiNewton methods to the unsmooth problem in a heurstic fashion. Our solver is one of the most consistently fast LASSO solvers (it also solves nonlinear leastsquares problems, among others), and is faster than wellknown algorithms like LBFGSB. This is also actively maintained on github under the BSD license. 
TFOCS Templates for FirstOrder Conic Solvers (2010)
A Matlab software package designed to solve all compressed sensing (and lowrank recovery) problems, but in fact it goes much farther and solves all conic programming problems. Joint work with Michael Grant and Emmanuel Candès. This is actively maintained, and under the BSD license. Paper 
NESTA Nesterov’s Algorithm (2009)
A Matlab software package designed to solve some constrained compressed sensing problems, when the measurement matrix is a partial isometry or not too large (however, the analysis dictionary may be very large). Joint work with Jerome Bobin and Emmanuel Candès. You can download the paper here: Paper. A local version of the package is hosted here: NESTA_v1.1.zip. 
SVD Singular Value Thresholding (2009)
A Matlab (with mex files) package for matrix completion via nuclearnorm minimization. Please email me if you have questions about the software (and include information on the verson of Matlab, the operating system, and the hardware – e.g. 32bit or 64bit). I am working on making it more compatible with 64bit systems and compatible with complexvalued data. We have experimental versions using Nesterov stepsizes and even LBFGS acceleration, but these are standard optimization tricks so we have not described them in papers. SVT is now one of the classic “reference” algorithms used in the field. The version provided is very simple and doesn’t use a line search feature, and may even diverge if you set the stepsize above the legal limit. For this reason, we recommend using TFOCS, which is a more powerful version of SVT. Paper (UPDATE: June 2019, I have put SVT code on github, but maintenance is minimal)
Misc. documentation

Parallel computing
For working on a cluster (especially a CU one), Richard has some tips 
BLAS
Here is a quick reference guide to BLAS in PDF which I have taken from netlib’s version and usedpkfixhelper
andpkfix
to make a PDF that actually has readable fonts.