## Description

ASP is a set of Matlab routines for solving several variations of the sparse optimization problem

$$\mathop{\mbox{minimize}}_{x} \quad \lambda\|x\|_1 + \frac12\|Ax-b\|_2^2$$

It implements algorithms for the following:

• basis pursuit denoising (including $$Ax=b$$)
• orthogonal matching pursuit
• homotopy version of basis pursuit denoising
• reweighted basis pursuit for approximating 0-norm solutions
• sequential compressed sensing (adding rows to $$A$$ and $$b$$)
• nonnegative least-squares
• sparse-residual and sparse-solution regression
• generalized Lasso for sparsity in $$Bx$$

## References

• M. P. Friedlander and M. A. Saunders (2012). A dual active-set quadratic programming method for finding sparse least-squares solutions, DRAFT Technical Report, Dept of Computer Science, University of British Columbia, July 30, 2012. PDF

• 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, 1181-1186. [This paper made use of ASP (via BPdual) as well as CVX, FISTA, SPGL1, and Mosek.]