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(), ...)
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 |
... |
additional arguments passed to the function. |
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.
List with components:
par |
the optimal solution found so far. |
value |
the function value corresponding to |
iter |
number of (outer) iterations, see |
convergence |
integer code indicating successful completion (> 0) or a possible error number (< 0). |
message |
character string produced by NLopt and giving additional information. |
The author of NLopt would tend to recommend the Subplex method instead.
Hans W. Borchers
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
# 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
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.