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An implementation of almost the original Nelder-Mead simplex algorithm.
neldermead(
x0,
fn,
lower = NULL,
upper = NULL,
nl.info = FALSE,
control = list(),
...
)
starting point for searching the optimum.
objective function that is to be minimized.
lower and upper bound constraints.
logical; shall the original NLopt info been shown.
list of options, see nl.opts
for help.
additional arguments passed to the function.
List with components:
the optimal solution found so far.
the function value corresponding to par
.
number of (outer) iterations, see maxeval
.
integer code indicating successful completion (> 0) or a possible error number (< 0).
character string produced by NLopt and giving additional information.
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.
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
# 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 {
# }
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