pracma (version 1.8.6)

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

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.

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.

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.

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(0,0,0,0), 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