neldermead function

Nelder-Mead Simplex

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

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.

Returns

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.

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.

Note

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

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)

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

Author(s)

Hans W. Borchers