极大似然估计

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One Dimensional Optimization

Description

The function optimize searches the interval from lower to upper for a minimum or maximum of the function f with respect to its first argument.

optimise is an alias for optimize.

Usage

optimize(f = , interval = ,  ..., lower = min(interval),
         upper = max(interval), maximum = FALSE,
         tol = .Machine$double.eps^0.25)
optimise(f = , interval = ,  ..., lower = min(interval),
         upper = max(interval), maximum = FALSE,
         tol = .Machine$double.eps^0.25)

Arguments

f	the function to be optimized. The function is either minimized or maximized over its first argument depending on the value of maximum.
interval	a vector containing the end-points of the interval to be searched for the minimum.
...	additional named or unnamed arguments to be passed to f.
lower	the lower end point of the interval to be searched.
upper	the upper end point of the interval to be searched.
maximum	logical. Should we maximize or minimize (the default)?
tol	the desired accuracy.

Value

A list with components minimum (or maximum) and objective which give the location of the minimum (or maximum) and the value of the function at that point.

Examples

require(graphics)

f <- function (x,a) (x-a)^2
xmin <- optimize(f, c(0, 1), tol = 0.0001, a = 1/3)
xmin

## See where the function is evaluated:
optimize(function(x) x^2*(print(x)-1), lower=0, upper=10)

## "wrong" solution with unlucky interval and piecewise constant f():
f  <- function(x) ifelse(x > -1, ifelse(x < 4, exp(-1/abs(x - 1)), 10), 10)
fp <- function(x) { print(x); f(x) }

plot(f, -2,5, ylim = 0:1, col = 2)
optimize(fp, c(-4, 20))# doesn't see the minimum
optimize(fp, c(-7, 20))# ok