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DESCRIPTION

Minimizes a, possibly non-smooth, user-supplied function using the Nelder-Mead Simplex Algorithm.

 

USAGE

neldmead(fobj, startvec, print.level=0, tol=1e-6, ...)

 

REQUIRED ARGUMENTS

fobj		real-valued function.
startvec		numeric vector of length 2 or greater. Initial value for the first argument of fobj.

 

OPTIONAL ARGUMENTS

print.level		Desired level of output during the iteration. Print.level = 0 for quiet running, = 1 for function value at each iteration, = 2 to prompt for continuation after each iteration.
tol		Desired accuracy.
...		Additional arguments to be passed to fobj.

 

VALUE

List with the following components:

x		numeric vector. Argument of fobj at the local minima.
fmin		value of fobj at the local minima.
iter		number of iterations used.

 

DETAILS

The Nelder-Mead simplex algorithm is an inefficient minimizer but it is not sensitive to starting values and does not rely on derivatives or even on continuity of the objective function. It is therefore useful for obtaining a decent starting point and scale information for one of the efficient methods, or for minimizing a non-smooth objective function which would not be suitable for the built-in S-Plus function nlmin.

 

The simplex method is applicable only to functions of several variables. If you want to minimize a continuous function of one variable, use the built-in S-Plus optimize instead.

 

AUTHOR

This function is a modified version of the function posted by Bill Clark to the S-News news group in March 1997. David Clifford of the University of Chicago corrected and improved the implementation of the algorithm.

 

REFERENCES

Press et al, Numerical Methods in C, page 305.

 

SEE ALSO

nlmin and optimize in the S-Plus documentation.

EXAMPLES

# Find a least trimmed SS (LTS) regression estimator
# neldmead is more accurate but slower than the built-in
# S-Plus function ltsreg

> x <- 1:20
> y <- x + rnorm(20)
> lts <- function(ab, x, y)
{
	e <- y - ab[1] - ab[2] * x
	trim <- floor(length(y)/2) + floor(length(ab)/2)
	mean(sort(e^2)[1:trim])
}
> neldmead(lts,c(0,0),x=x,y=y)
$x:
[1] -0.09447435 1.00664786

$fmin:
[1] 0.04699288

$iter:
[1] 50

 

Gordon Smyth. Copyright © 1996-2016. Last modified: 10 February 2004