pracma (version 1.7.0)

hooke-jeeves: Hooke-Jeeves Method

Description

An implementation of the Hooke-Jeeves algorithm for derivative-free optimization.

Usage

hooke_jeeves(x0, f, h = 1, scale = 1,
             info = FALSE, tol = .Machine$double.eps^(2/3), ...)

Arguments

x0

start value.

f

function to be minimized.

h

starting step size.

scale

scale factor, of -1 the maximum will be searched for.

info

logical, whether to print information during the main loop.

tol

relative tolerance, to be used as stopping rule.

...

additional arguments to be passed to the function.

Value

• List with following components:
• xmin
  minimum solution found.
• fmin
  value of f at minimum.
• fcalls
  number of function calls.
• niter
  number of iterations performed.

Details

This method computes a new point using the values of f at suitable points along the orthogonal coordinate directions around the last point.

References

Quarteroni, Sacco, and Saleri (2007), Numerical Mathematics, Springer.

See Also

nelder_mead

Examples

##  Rosenbrock function
rosenbrock <- function(x) {
    n <- length(x)
    x1 <- x[2:n]
    x2 <- x[1:(n-1)]
    sum(100*(x1-x2^2)^2 + (1-x2)^2)
}
hooke_jeeves(c(0, 0), rosenbrock)
# $xmin
# [1] 1 1
# $fmin
# [1] 1.328283e-16
# $fcalls
# [1] 31934
# $niter
# [1] 4344