# neldermead

##### Nelder-Mead Simplex

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:

the optimal solution found so far.

the function value corresponding to `par`

.

number of (outer) iterations, see `maxeval`

.

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

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).

##### See Also

`dfoptim::nmk`

##### Examples

```
# NOT RUN {
# Fletcher and Powell's helic valley
fphv <- function(x)
100*(x[3] - 10*atan2(x[2], x[1])/(2*pi))^2 +
(sqrt(x[1]^2 + x[2]^2) - 1)^2 +x[3]^2
x0 <- c(-1, 0, 0)
neldermead(x0, fphv) # 1 0 0
# Powell's Singular Function (PSF)
psf <- function(x) (x[1] + 10*x[2])^2 + 5*(x[3] - x[4])^2 +
(x[2] - 2*x[3])^4 + 10*(x[1] - x[4])^4
x0 <- c(3, -1, 0, 1)
neldermead(x0, psf) # 0 0 0 0, needs maximum number of function calls
# }
# NOT RUN {
# Bounded version of Nelder-Mead
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*