NR function

Newton-Raphson method

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))