# L1-norm regularized least-squares¶

We consider a least-squares problem with -norm regularization

(1)¶

with variable and problem data and . The problem is equivalent to a QP

(2)¶

with variables and constraints. The problem can also be written as a separable QP

(3)¶

### Documentation

Solvers for the -norm regularized least-squares problem are
available as a Python module `l1regls.py`

(or `l1regls_mosek6.py`

or `l1regls_mosek7.py`

for earlier versions of CVXOPT that use MOSEK 6 or 7). The module implements the following three functions:

### Example

```
from l1regls import l1regls
from cvxopt import normal
m, n = 50, 200
A, b = normal(m,n), normal(m,1)
x = l1regls(A,b)
```