nloptr (version 2.0.3)

neldermead: 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.

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.

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.

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
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
# }
# NOT RUN {
# }