### Introduction

**FPC_AS** (fixed-point continuation and active set) is a MATLAB solver for the l1-regularized least squares problem

minimize_{x} mu||*x*||_{1} + (1/2)||*Ax*-*b*||_{2}^{2},

where the parameter mu, the matrix *A*, and the vector *b* are given. This problem arises in compressed sensing to recover a sparse vector *x** from a set of linear measurements *b*=*Ax** or *b*=*Ax**+**n**, where **n** is noise. The measurements can be incomplete (or undersampled) to certain degree in the sense that *b* has less number of components than *x*.

This solver can also solve the contrained problem

minimize_{x} ||*x*||_{1}, subject to *Ax*=*b*,

if mu is set to be a tiny value (e.g., 1E-10).

For more information about the theory and applications of these problems, see the review article [pdf].