# SLOPE_solver: Sorted L1 solver

Description Usage Arguments Details Value

### Description

Solves the sorted L1 penalized regression problem: given a matrix A, a vector b, and a decreasing vector λ, find the vector x minimizing

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

### Usage

 1 2 3 SLOPE_solver(A, b, lambda, initial = NULL, prox = prox_sorted_L1, max_iter = 10000, grad_iter = 20, opt_iter = 1, tol_infeas = 1e-06, tol_rel_gap = 1e-06) 

### Arguments

 A an n-by-p matrix b vector of length n lambda vector of length p, sorted in decreasing order initial initial guess for x prox function that computes the sorted L1 prox max_iter maximum number of iterations in the gradient descent grad_iter number of iterations between gradient updates opt_iter number of iterations between checks for optimality tol_infeas tolerance for infeasibility tol_rel_gap tolerance for relative gap between primal and dual problems

### Details

This optimization problem is convex and is solved using an accelerated proximal gradient descent method.

### Value

An object of class SLOPE_solver.result. This object is a list containing at least the following components:

 x solution vector x optimal logical: whether the solution is optimal iter number of iterations

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