ADMM_EN_SMW: ADMM on l1 regularized quadratic program

View source: R/ADMM_EN_SMW.R

ADMM_EN_SMWR Documentation

ADMM on l1 regularized quadratic program

Description

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

Usage

ADMM_EN_SMW(Ainv, V, R, d, x0, lam, mu, maxits, tol, quiet, selector)

Arguments

Ainv

Diagonal of A^{-1} term in SMW formula, where A is an n by n positive definite coefficient matrix.

V

Matrix from SMW formula.

R

Upper triangular matrix in Cholesky decomposition of I + UA^{-1}V.

d

nx1 dimensional column vector.

lam

Regularization parameter for l1 penalty, must be greater than zero.

mu

Augmented Lagrangian penalty parameter, must be greater than zero.

maxits

Number of iterations to run

tol

Vector of stopping tolerances, first value is absolute, second is relative tolerance.

quiet

Logical controlling display of intermediate statistics.

selector

Vector to choose which parameters in the discriminant vector will be used to calculate the regularization terms. The size of the vector must be *p* the number of predictors. The default value is a vector of all ones. This is currently only used for ordinal classification.

Details

This function is used by other functions and should only be called explicitly for debugging purposes.

Value

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.

See Also

Used by: SDAD and the SDADcv cross-validation version.


gumeo/accSDA documentation built on Nov. 16, 2023, 11:47 p.m.