Applies Alternating Direction Method of Multipliers to the l1-regularized quadratic program $$f(\mathbf{x}) + g(\mathbf{x}) = \frac{1}{2}\mathbf{x}^TA\mathbf{x} - d^T\mathbf{x} + \lambda |\mathbf{x}|_1$$
ADMM_EN_SMW(Ainv, V, R, d, x0, lam, mu, maxits, tol, quiet)
Diagonal of \(A^{-1}\) term in SMW formula, where A is an n by n positive definite coefficient matrix.
Matrix from SMW formula.
Upper triangular matrix in Cholesky decomposition of \(I + UA^{-1}V\).
nx1 dimensional column vector.
Regularization parameter for l1 penalty, must be greater than zero.
Augmented Lagrangian penalty parameter, must be greater than zero.
Number of iterations to run
Vector of stopping tolerances, first value is absolute, second is relative tolerance.
Logical controlling display of intermediate statistics.
Step length.
ADMM_EN_SMW
returns an object of class
"ADMM_EN_SMW
" including a list
with the following named components
call
The matched call.
x
Found solution.
y
Dual solution.
z
Slack variables.
k
Number of iterations used.
This function is used by other functions and should only be called explicitly for debugging purposes.
Used by: SDAD
and the SDADcv
cross-validation version.