hookejeeves {adagio}

Hooke-Jeeves Minimization Method

Description

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

Usage

hookejeeves(x0, f, lb = NULL, ub = NULL,
            tol = 1e-08,
            target = Inf, maxfeval = Inf, info = FALSE, ...)

Arguments

x0

starting vector.

f

nonlinear function to be minimized.

lb, ub

lower and upper bounds.

tol

relative tolerance, to be used as stopping rule.

target

iteration stops when this value is reached.

maxfeval

maximum number of allowed function evaluations.

info

logical, whether to print information during the main loop.

...

additional arguments to be passed to the function.

Details

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

Value

List with following components:

xmin

minimum solution found so far.

fmin

value of f at minimum.

fcalls

number of function evaluations.

niter

number of iterations performed.

Note

Hooke-Jeeves is notorious for its number of function calls. Memoization is often suggested as a remedy.

For a similar implementation of Hooke-Jeeves see the ‘dfoptim’ package.

References

C.T. Kelley (1999), Iterative Methods for Optimization, SIAM.

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

See Also

neldermead

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)
}

hookejeeves(c(0,0,0,0), rosenbrock)
# $xmin
# [1] 1.000000 1.000001 1.000002 1.000004
# $fmin
# [1] 4.774847e-12
# $fcalls
# [1] 2499
# $niter
#[1] 26

hookejeeves(rep(0,4), lb=rep(-1,4), ub=0.5, rosenbrock)
# $xmin
# [1] 0.50000000 0.26221320 0.07797602 0.00608027
# $fmin
# [1] 1.667875
# $fcalls
# [1] 571
# $niter
# [1] 26