ADMM in scaled form for the LASSO

x <- (X'X + rho I)^{-1}(X'y + rho(z - u)); z <- S_{lam/rho}(x + u); u <- u + x - z.

Usage

Admmlasso(X, y, lam, rho = 1, steps = 100)

Arguments

X

Design matrix.

y

Response of length n.

lam

L1 penalty, non-negative.

rho

Augmented-Lagrangian parameter, strictly positive.

steps

Fixed iteration count.

Value

List with x, z, u, objective, primalres, dualres, rho, steps, n, p.

References

Boyd, Parikh, Chu, Peleato and Eckstein (2011), Foundations and Trends in Machine Learning 3(1), Sect. 6.4 and Sect. 3.1.1; standard published form.

Examples

Admmlasso(X = c(1, 2, 3, 4, 5, 6, 7, 8), y = c(1, 2, 3, 4, 5, 6, 7, 8), lam = 5L)
#> $x
#> [1] 0.9754902
#> 
#> $z
#> [1] 0.9754902
#> 
#> $u
#> [1] 5
#> 
#> $objective
#> [1] 4.938725
#> 
#> $primalres
#> [1] 1.110223e-16
#> 
#> $dualres
#> [1] 0
#> 
#> $rho
#> [1] 1
#> 
#> $steps
#> [1] 100
#> 
#> $n
#> [1] 8
#> 
#> $p
#> [1] 1
#> 
#> $method
#> [1] "ADMM for the LASSO, scaled form (Boyd et al. 2011 Sect. 6.4)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"