SPGL1: Spectral Projected Gradient for L1 minimization
Original home page: http://www.cs.ubc.ca/labs/scl/spgl1/
Introduction
SPGL1 is a solver for largescale onenorm regularized least squares.
It is designed to solve any of the following three problems:

Basis pursuit denoise (BPDN):
minimize x_1 subject to Ax  b_2 <= sigma
, 
Basis pursuit (BP):
minimize x_1 subject to Ax = b

Lasso:
minimize Ax  b_2 subject to x_1 <= tau
,
The matrix A
can be defined explicitly, or as an operator
that returns both both Ax
and A'b
.
SPGL1 can solve these three problems in both the real and complex domains.
Installation
From PyPi
If you want to use spgl1
within your codes, install it in your
Python environment by typing the following command in your terminal:
pip install spgl1
From Source
First of all clone the repo. To install spgl1
within your current
environment, simply type:
make install
or as a developer:
make devinstall
To install spgl1
in a new conda environment, type:
make install_conda
or as a developer:
make devinstall_conda
Getting started
Examples can be found in the examples
folder in the form of
jupyter notebooks.
Documentation
The official documentation is built with Sphinx and hosted on readthedocs.
References
The algorithm implemented by SPGL1 is described in these two papers

E. van den Berg and M. P. Friedlander, "Probing the Pareto frontier for basis pursuit solutions", SIAM J. on Scientific Computing, 31(2):890912, November 2008

E. van den Berg and M. P. Friedlander, "Sparse optimization with leastsquares constraints", Tech. Rep. TR201002, Dept of Computer Science, Univ of British Columbia, January 2010