neldermead {nloptr}

Nelder-Mead Simplex

Description

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 explicit 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.

Author(s)

Hans W. Borchers

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

# 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
rosenbrock <- function(x) { ## Rosenbrock Banana function
  100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2 +
  100 * (x[3] - x[2]^2)^2 + (1 - x[2])^2
}
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
## End(Not run)