Finding Function Minimum

Find minimum of single-variable function on fixed interval.

fminbnd(f, a, b, maxiter = 1000, maximum = FALSE,
        tol = 1e-07, rel.tol = tol, abs.tol = 1e-15, ...)

Arguments

f

function whose minimum or maximum is to be found.

a, b

endpoints of the interval to be searched.

maxiter

maximal number of iterations.

maximum

logical; shall maximum or minimum be found; default FALSE.

tol

relative tolerance; left over for compatibility.

rel.tol, abs.tol

relative and absolute tolerance.

...

additional variables to be passed to the function.

Details

fminbnd finds the minimum of a function of one variable within a fixed interval. It applies Brent's algorithm, based on golden section search and parabolic interpolation.

fminbnd may only give local solutions. fminbnd never evaluates f at the endpoints.

Value

List with

xmin

location of the minimum resp. maximum.

fmin

function value at the optimum.

niter

number of iterations used.

estim.prec

estimated precision.

References

R. P. Brent (1973). Algorithms for Minimization Without Derivatives. Dover Publications, reprinted 2002.

Note

fminbnd mimics the Matlab function of the same name.

See also

fibsearch, golden_ratio

Examples

##  CHEBFUN example by Trefethen
f <- function(x) exp(x)*sin(3*x)*tanh(5*cos(30*x))
fminbnd(f, -1, 1)                   # fourth local minimum (from left)
#> $xmin
#> [1] -0.2429114
#> 
#> $fmin
#> [1] -0.517464
#> 
#> $niter
#> [1] 17
#> 
#> $estim.prec
#> [1] 2.429114e-08
#> 
g <- function(x) complexstep(f, x)  # complex-step derivative
xs <- findzeros(g, -1, 1)           # local minima and maxima
ys <- f(xs); n0 <- which.min(ys)    # index of global minimum
fminbnd(f, xs[n0-1], xs[n0+1])      # xmin:0.7036632, fmin: -1.727377
#> $xmin
#> [1] 0.7036632
#> 
#> $fmin
#> [1] -1.727377
#> 
#> $niter
#> [1] 14
#> 
#> $estim.prec
#> [1] 7.036632e-08
#> 

if (FALSE) { # \dontrun{
ezplot(f, -1, 1, n = 1000, col = "darkblue", lwd = 2)
ezplot(function(x) g(x)/150, -1, 1, n = 1000, col = "darkred", add = TRUE)
grid()} # }