Solves the sorted L1 penalized regression problem: given a matrix \(A\), a vector \(b\), and a decreasing vector \(\lambda\), find the vector \(x\) minimizing $$\frac{1}{2}\Vert Ax - b \Vert_2^2 + \sum_{i=1}^p \lambda_i |x|_{(i)}.$$ This optimization problem is convex and is solved using an accelerated proximal gradient descent method.
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
)An object of class SLOPE_solver.result. This object is a list
containing at least the following components:
solution vector \(x\)
logical: whether the solution is optimal
number of iterations
an \(n\)-by-\(p\) matrix
vector of length \(n\)
vector of length \(p\), sorted in decreasing order
initial guess for \(x\)
function that computes the sorted L1 prox
maximum number of iterations in the gradient descent
number of iterations between gradient updates
number of iterations between checks for optimality
tolerance for infeasibility
tolerance for relative gap between primal and dual problems
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.