https://github.com/cran/pracma
Tip revision: 7ba95550c2066826c77bc78b974b7cb8cd416301 authored by Hans W. Borchers on 11 January 2017, 00:43:13 UTC
version 1.9.9
version 1.9.9
Tip revision: 7ba9555
steep_descent.Rd
\name{steep_descent}
\alias{steep_descent}
\title{
Steepest Descent Minimization
}
\description{
Function minimization by steepest descent.
}
\usage{
steep_descent(x0, f, g = NULL, info = FALSE,
maxiter = 100, tol = .Machine$double.eps^(1/2))
}
\arguments{
\item{x0}{start value.}
\item{f}{function to be minimized.}
\item{g}{gradient function of \code{f};
if \code{NULL}, a numerical gradient will be calculated.}
\item{info}{logical; shall information be printed on every iteration?}
\item{maxiter}{max. number of iterations.}
\item{tol}{relative tolerance, to be used as stopping rule.}
}
\details{
Steepest descent is a line search method that moves along the downhill
direction.
}
\value{
List with following components:
\item{xmin}{minimum solution found.}
\item{fmin}{value of \code{f} at minimum.}
\item{niter}{number of iterations performed.}
}
\references{
Nocedal, J., and S. J. Wright (2006). Numerical Optimization.
Second Edition, Springer-Verlag, New York, pp. 22 ff.
}
\note{
Used some Matlab code as described in the book ``Applied Numerical Analysis
Using Matlab'' by L. V.Fausett.
}
\seealso{
\code{\link{fletcher_powell}}
}
\examples{
## Rosenbrock function: The flat valley of the Rosenbruck function makes
## it infeasible for a steepest descent approach.
# rosenbrock <- function(x) {
# n <- length(x)
# x1 <- x[2:n]
# x2 <- x[1:(n-1)]
# sum(100*(x1-x2^2)^2 + (1-x2)^2)
# }
# steep_descent(c(1, 1), rosenbrock)
# Warning message:
# In steep_descent(c(0, 0), rosenbrock) :
# Maximum number of iterations reached -- not converged.
## Sphere function
sph <- function(x) sum(x^2)
steep_descent(rep(1, 10), sph)
# $xmin 0 0 0 0 0 0 0 0 0 0
# $fmin 0
# $niter 2
}
\keyword{ optimize }