hookejeeves: Hooke-Jeeves Minimization Method

In adagio: Discrete and Global Optimization Routines

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

adagio documentation built on Oct. 26, 2023, 5:08 p.m.