Revision d50cda4811eb3cdb8d2ce9e01ddb5e07d4a8c24f authored by HwB on 11 September 2013, 00:00:00 UTC, committed by Gabor Csardi on 11 September 2013, 00:00:00 UTC
1 parent 10ae2bb
direct1d.Rd
\name{direct1d}
\alias{direct1d}
\title{
Univariate Global Optimization
}
\description{
Implementation of the DIRECT global optimization algorithm in the
one-dimensional case.
}
\usage{
direct1d(f, a, b, maxiter = 20, ...)
}
\arguments{
\item{f}{function to be minimized.}
\item{a, b}{end points of the interval, \code{a<b}.}
\item{maxiter}{maximum number of iterations.}
\item{...}{further parameters to be passed to the function.}
}
\details{
The DIRECT algorithm for the one-dimensional case is directly derived from
Shubert's algorithm. Instead of computing the function at the endpoints of
the interval, it is computed at the midpoint. Intervals ar split in three
parts, sparing one function evaluation.
}
\value{
List with components \code{xmin} and \code{fmin}, the minimum found so far
and its function value.
}
\note{
The subroutine for finding the set of optimal subintervals is slow and
has to be intelligently refitted.
}
\author{
HwB email: <hwborchers@googlemail.com>
}
\references{
Jones, D. R., C. D. Perttunen, and B. E. Stuckman (1993). Lipschitzian
Optimization Without the Lipschitz Constant. Journal of Optimization
Theory and Application, Vol. 79. No. 1, pp. 157ff.
Finkel, D., and C. Kelley (2006). Additive Scaling and the DIRECT Algorithm.
Journal of Global Optimization, Vol. 36, No. 4, pp. 597--608.
}
\seealso{
\code{\link{findmins}}, \code{dfoptim::direct}
}
\examples{
f <- function(x) sin(10*pi*x) + 0.5*(x-0.5)^2
a <- 0; b <- 1
direct1d(f, 0, 1, maxiter = 20)
# $xmin: 0.5499493794 (error: 3.5e-6)
# $fmin: -0.9987512652
\dontrun{
ezplot(f, a, b, 1000)}
}
\keyword{ optimize }
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