hooke_jeeves: Hooke-Jeeves Minimization Method

Description

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

Usage

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

Arguments

starting vector.

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.

Value

List with following components:

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

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

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

Examples

Run this code

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

hooke_jeeves(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

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