Newton-Raphson method
Newton-Raphson method
NR( start, objective = NULL, gradient = NULL, hessian = NULL, control, args = NULL, ... )
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 |
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)
# 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))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.