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, ...)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. |
This method computes a new point using the values of f at suitable
points along the orthogonal coordinate directions around the last point.
List with following components:
xmin |
minimum solution found so far. |
fmin |
value of |
fcalls |
number of function evaluations. |
niter |
number of iterations performed. |
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.
C.T. Kelley (1999), Iterative Methods for Optimization, SIAM.
Quarteroni, Sacco, and Saleri (2007), Numerical Mathematics, Springer-Verlag.
## 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] 26Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.