NR: Newton-Raphson method

In kkholst/lava: Latent Variable Models

Newton-Raphson method

Description

Newton-Raphson method

Usage

NR(
  start,
  objective = NULL,
  gradient = NULL,
  hessian = NULL,
  control,
  args = NULL,
  ...
)

Arguments

start	Starting value
objective	Optional objective function (used for selecting step length)
gradient	gradient
hessian	hessian (if NULL a numerical derivative is used)
control	optimization arguments (see details)
args	Optional list of arguments parsed to objective, gradient and hessian
...	additional arguments parsed to lower level functions

Details

control should be a list with one or more of the following components:

• trace integer for which output is printed each 'trace'th iteration

• iter.max number of iterations

• stepsize: Step size (default 1)

• nstepsize: Increase stepsize every nstepsize iteration (from stepsize to 1)

• tol: Convergence criterion (gradient)

• epsilon: threshold used in pseudo-inverse

• backtrack: In each iteration reduce stepsize unless solution is improved according to criterion (gradient, armijo, curvature, wolfe)

Examples

# Objective function with gradient and hessian as attributes
f <- function(z) {
   x <- z[1]; y <- z[2]
   val <- x^2 + x*y^2 + x + y
   structure(val, gradient=c(2*x+y^2+1, 2*y*x+1),
             hessian=rbind(c(2,2*y),c(2*y,2*x)))
}
NR(c(0,0),f)

# Parsing arguments to the function and
g <- function(x,y) (x*y+1)^2
NR(0, gradient=g, args=list(y=2), control=list(trace=1,tol=1e-20))

kkholst/lava documentation built on Jan. 13, 2025, 12:34 p.m.