Algorithm 5 Iterative SLOPE fitting when σ is unknown
1:	input: y, X and initial sequence λS (computed for σ = 1)
2:	initialize: S+ = ∅
3:	repeat
4:	S = S+
5:	compute the RSS obtained by regressing y onto variables in S
6:	set ${\widehat{\sigma }}^2=\text{RSS}/\left(n-|S|-1\right)$
7:	compute the solution $\widehat{\beta }$ to SLOPE with parameter sequence $\widehat{\sigma }\cdot {\mathrm{\lambda }}^S$
8:	set $S_{+}=\text{supp}\left(\widehat{\beta }\right)$
9:	until S+ = S