Description Usage Arguments Details Value Note References See Also Examples
An implementation of almost the original Nelder-Mead simplex algorithm.
1 2 |
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.
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).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | # 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)
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