0th

Percentile

An implementation of almost the original Nelder-Mead simplex algorithm.

##### Usage
neldermead(x0, fn, lower = NULL, upper = NULL, nl.info = FALSE,
control = list(), ...)
##### Arguments
x0

starting point for searching the optimum.

fn

objective function that is to be minimized.

lower, upper

lower and upper bound constraints.

nl.info

logical; shall the original NLopt info been shown.

control

list of options, see nl.opts for help.

...

additional arguments passed to the function.

##### Details

Provides xplicit support for bound constraints, using essentially the method proposed in [Box]. Whenever a new point would lie outside the bound constraints the point is moved back exactly onto the constraint.

##### Value

List with components:

par

the optimal solution found so far.

value

the function value corresponding to par.

iter

number of (outer) iterations, see maxeval.

convergence

integer code indicating successful completion (> 0) or a possible error number (< 0).

message

character string produced by NLopt and giving additional information.

##### Note

The author of NLopt would tend to recommend the Subplex method instead.

##### References

J. A. Nelder and R. Mead, A simplex method for function minimization,'' The Computer Journal 7, p. 308-313 (1965).

M. J. Box, A new method of constrained optimization and a comparison with other methods,'' Computer J. 8 (1), 42-52 (1965).

dfoptim::nmk

##### Examples
# NOT RUN {
# Fletcher and Powell's helic valley
fphv <- function(x)
100*(x - 10*atan2(x, x)/(2*pi))^2 +
(sqrt(x^2 + x^2) - 1)^2 +x^2
x0 <- c(-1, 0, 0)
neldermead(x0, fphv)    #  1 0 0

# Powell's Singular Function (PSF)
psf <- function(x)  (x + 10*x)^2 + 5*(x - x)^2 +
(x - 2*x)^4 + 10*(x - x)^4
x0 <- c(3, -1, 0, 1)
neldermead(x0, psf)     #  0 0 0 0, needs maximum number of function calls

# }
# NOT RUN {
lower <- c(-Inf, 0,   0)
upper <- c( Inf, 0.5, 1)
x0 <- c(0, 0.1, 0.1)
S <- neldermead(c(0, 0.1, 0.1), rosenbrock, lower, upper, nl.info = TRUE)
# $xmin = c(0.7085595, 0.5000000, 0.2500000) #$fmin = 0.3353605
# }
# NOT RUN {
# }

Documentation reproduced from package nloptr, version 1.2.1, License: LGPL-3

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