Golden Ratio Search

Golden Ratio search for a univariate function minimum in a bounded interval.

golden_ratio(f, a, b, ..., maxiter = 100, tol = .Machine$double.eps^0.5)

Arguments

f

Function or its name as a string.

a, b

endpoints of the interval.

maxiter

maximum number of iterations.

tol

absolute tolerance; default sqrt(eps).

...

Additional arguments to be passed to f.

Details

`Golden ratio' search for a univariate function minimum in a bounded interval.

Value

Return a list with components xmin, fmin, the function value at the minimum, niter, the number of iterations done, and the estimated precision estim.prec

See also

uniroot

Examples

f <- function(x) x * cos(0.1*exp(x)) * sin(0.1*pi*exp(x))
golden_ratio(f, 0, 4, tol=10^-10)  # $xmin    = 3.24848329206212
#> $xmin
#> [1] 3.248483
#> 
#> $fmin
#> [1] -2.665089
#> 
#> $iter
#> [1] 48
#> 
#> $estim.prec
#> [1] 8.783951e-11
#> 
optimize(f, c(0,4), tol=10^-10)    # $minimum = 3.24848328971188
#> $minimum
#> [1] 3.248483
#> 
#> $objective
#> [1] -2.665089
#>