Systems Optimization Laboratory
Stanford, CA 943054121 USA

ASP: Sparse Optimization
 AUTHORS:
Michael Friedlander and
Michael Saunders.
 CONTENTS: A set of Matlab routines for solving several variations
of the sparse optimization problem
\begin{align*}
\text{minimize } & \lambda \x\_1 + \frac12 \Axb\_2^2,
\end{align*}
where \(A\) may be an explicit dense or sparse rectangular
matrix or an operator for computing \(Av\) and \(A^T u\)
for given vectors \(v, u\).
There are functions for the following problems:
 basis pursuit denoising (BPDN), including \(Ax=b\) (BP)
 orthogonal matching pursuit
 homotopy version of basis pursuit denoising
 reweighted basis pursuit for approximating 0norm solutions
 sequential compressed sensing
(adding rows to \(A\) and \(b\))
 nonnegative leastsquares
 sparseresidual and sparsesolution regression
 generalized Lasso for sparsity in \(Bx\)
For certain matching values of \(\lambda\) and \(\tau\),
BPDN is equivalent to the Lasso problem:
minimize \(\frac12 \Axb\_2^2\)
subject to \(\x\_1 \le \tau\).
 REFERENCES:
[1] Michael Friedlander and Michael Saunders (2012).
A dual activeset quadratic programming method
for finding sparse leastsquares solutions,
DRAFT Technical Report, Dept of Computer Science,
University of British Columbia, July 30, 2012.
[2] Hatef Monajemi, Sina Jafarpour, Matan Gavish,
Stat 330/CME 362 Collaboration and David L. Donoho (2012).
Deterministic matrices matching the compressed sensing
phase transitions of Gaussian random matrices,
PNAS 110:4, 11811186.
This paper made use of ASP (via BPdual) as well as
CVX, FISTA, SPGL1, and Mosek.
 RELEASE:
17 Dec 2012: aspv1.0.zip downloadable
from Michael Friedlander's homepage.
14 May 2015: BPprimal.m added to zip.
26 May 2015:
asp is now a Git repository.
DOWNLOADS:
