prox_sorted_L1 {grpSLOPE}

Prox for sorted L1 norm

Description

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

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

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.

Usage

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

Arguments

x

input vector

lambda

vector of \lambda's, sorted in decreasing order

method

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

Details

This function has been adapted (with only cosmetic changes) from the R package SLOPE version 0.1.3, due to this function being deprecated and defunct in SLOPE versions which are newer than 0.1.3.

Value

The solution vector y.