APG_EN2bt: Accelerated Proximal Gradient (with backtracking) on l1...
In gumeo/accSDA: Accelerated Sparse Discriminant Analysis

APG_EN2bt

R Documentation

Accelerated Proximal Gradient (with backtracking) on l1 regularized quadratic program

Applies accelerated proximal gradient algorithm (with backtracking) 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

APG_EN2bt(
  A,
  Xt,
  Om,
  gamma,
  d,
  x0,
  lam,
  L,
  eta,
  maxits,
  tol,
  selector = rep(1, dim(x0)[1])
)

`A`	p by p positive definite coefficient matrix `A = (\gamma Om + X^T X/n)` .
`Xt`	Same as X above, we need it to make calculations faster.
`Om`	Same reason as for the above parameter.
`gamma`	l2 regularizing parameter.
`d`	nx1 dimensional column vector.
`lam`	Regularization parameter for l1 penalty, must be greater than zero.
`L`	Initial vlaue of the backtracking Lipshitz constant.
`eta`	Backtracking scaling parameter.
`maxits`	Number of iterations to run
`tol`	Stopping tolerance for proximal gradient algorithm.
`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.

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

APG_EN2bt returns an object of class "APG_EN2bt" including a list with the following named components