# 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:

l1regls(A, b)

Solves the problem (2) using a custom KKT solver.

Returns the solution .

l1regls_mosek(A, b)

Solves the problem (2) using MOSEK. This function is only available if MOSEK is installed.

Returns the solution .

l1regls_mosek2(A, b)

Solves the problem (3) using MOSEK. This function is only available if MOSEK is installed.

Returns the solution .

### 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)