SPGL1: Spectral Projected Gradient for L1 minimization

Introduction

SPGL1 is a solver for large-scale one-norm 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.

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

First of all clone the repo. To install spgl1 within your current environment, simply type:

make install

or as a developer:

make dev-install

To install spgl1 in a new conda environment, type:

make install_conda

or as a developer:

make dev-install_conda

Examples can be found in the examples folder in the form of jupyter notebooks.

The official documentation is built with Sphinx and hosted on readthedocs.

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):890-912, November 2008
E. van den Berg and M. P. Friedlander, "Sparse optimization with least-squares constraints", Tech. Rep. TR-2010-02, Dept of Computer Science, Univ of British Columbia, January 2010