CVXGEN: Code Generation for Convex Optimization

Example: Lasso

This example, from statistics, demonstrates the lasso procedure ( ell_1 -regularized least squares). For some more details, see Boyd and Vandenberghe, 6.3.2.

Optimization problem

We wish to solve the optimization problem

$begin{array}{ll} mbox{minimize} & (1/2)|Ax - b|_2^2 + lambda |x|_1 end{array}$

with parameters

$A in mathbf{R}^{m times n}$
$b in mathbf{R}^m$
$lambda in mathbf{R}_+$

and optimization variable

$x in mathbf{R}^n$

The problem is interesting both when m < n , and when m > n .

CVXGEN code

dimensions
  m = 100
  n = 10
end

parameters
  A (m,n)
  b (m)
  lambda nonnegative  # regularization weight.
end

variables
  x (n)
end

minimize
  (1/2)*quad(A*x - b) + lambda*norm_1(x)
end