SLOPE_solver {SLOPE} | R Documentation |
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)}.
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)
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 |
This optimization problem is convex and is solved using an accelerated proximal gradient descent method.
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 |