prox_sorted_L1: Prox for sorted L1 norm

In grpSLOPE: Group Sorted L1 Penalized Estimation

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.

grpSLOPE documentation built on June 29, 2025, 5:07 p.m.