Algorithm 2.

Coordinate Descent

Input: x = 0, λ > 0, β = ATb

Output: x

while not converged do

x̃ = Sλ (β)1; j = arg maxi |xi − x̃i|, where i is the index of the component in x and x̃; $x_i^{k+1}=x_i^k$, i ≠ j, and $x_j^{k+1}={\stackrel{\sim }{x}}_j$; ${\beta }^{k+1}={\beta }^k-\mid x_j^k-{\stackrel{\sim }{x}}_j\mid {(A^{T}A)}_j$, and ${\beta }_j^{k+1}={\beta }_j^k$, where (AT A)j is the jth column of (AT A).

end while