hookejeeves: Hooke-Jeeves Function Minimization Method

In pracma: Practical Numerical Math Functions

Hooke-Jeeves Function Minimization Method

Description

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

Usage

hooke_jeeves(x0, fn, ..., lb = NULL, ub = NULL, tol = 1e-08,
             maxfeval = 10000, target = Inf, info = FALSE)

Arguments

x0	starting vector.
fn	nonlinear function to be minimized.
...	additional arguments to be passed to the function.
lb, ub	lower and upper bounds.
tol	relative tolerance, to be used as stopping rule.
maxfeval	maximum number of allowed function evaluations.
target	iteration stops when this value is reached.
info	logical, whether to print information during the main loop.

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.
count	number of function evaluations.
convergence	NOT USED at the moment.
info	special info from the solver.

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

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] 1.000002 1.000003 1.000007 1.000013
## $fmin
## [1] 5.849188e-11
## $count
## [1] 1691
## $convergence
## [1] 0
## $info
## $info$solver
## [1] "Hooke-Jeeves"
## $info$iterations
## [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
## $count
## [1] 536
## $convergence
## [1] 0
## $info
## $info$solver
## [1] "Hooke-Jeeves"
## $info$iterations
## [1] 26

pracma documentation built on Nov. 10, 2023, 1:14 a.m.