hookejeeves function

Hooke-Jeeves Minimization Method

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

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.

Returns

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.

References

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

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

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.

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