prox_sorted_L1 {SLOPE}R Documentation

Prox for sorted L1 norm

Description

Compute the prox for the sorted L1 norm. That is, given a vector x and a decreasing vector λ, compute the unique value of y minimizing

\frac{1}{2} \Vert x - y \Vert_2^2 + ∑_{i=1}^n λ_i |x|_{(i)}.

Usage

prox_sorted_L1(x, lambda, method = c("c", "isotone"))

Arguments

x

input vector

lambda

vector of λ's, sorted in decreasing order

method

underlying prox implementation, either 'c' or 'isotone' (see Details)

Details

At present, two methods for computing the sorted L1 prox are supported. By default, we use a fast custom C implementation. Since SLOPE can be viewed as an isotonic regression problem, the prox can also be computed using the isotone package. This option is provided primarily for testing.


[Package SLOPE version 0.1.3 Index]