fmin (MATLAB Function Reference)

fmin	Examples See Also

Minimize a function of one variable

NOTE
The name of this function has been changed to fminbnd in Release 11 (MATLAB 5.3). While fmin is supported in Release 11, it will be removed in a future release so please begin using fminbnd.

Syntax

x = fmin('fun',x1,x2)
x = fmin('fun',x1,x2,options)
x = fmin('fun',x1,x2,options,P1,P2, ...)
[x,options] = fmin(...)

Description

x = fmin('fun',x1,x2)

returns a value of x which is a local minimizer of fun(x) in the interval

x = fmin('fun',x1,x2,options)

does the same as the above, but uses options control parameters.

x = fmin('fun',x1,x2,options,P1,P2,...)

does the same as the above, but passes arguments to the objective function, fun(x,P1,P2,...). Pass an empty matrix for options to use the default value.

[x,options] = fmin(...)

returns, in options(10), a count of the number of steps taken.

Arguments


`x1,x2`	Interval over which `function` is minimized.
`P1,P2...`	Arguments to be passed to `function`.
`fun`	A string containing the name of the function to be minimized.
`options`	A vector of control parameters. Only three of the 18 components of `options` are referenced by `fmin`; Optimization Toolbox functions use the others. The three control `options` used by `fmin` are: `options(1)` -- If this is nonzero, intermediate steps in the solution are displayed. The default value of `options(1)` is 0. `options(2)` -- This is the termination tolerance. The default value is `1.e-4`. `options(14)` -- This is the maximum number of steps. The default value is `500`.

Examples

fmin('cos',3,4) computes

to a few decimal places.

fmin('cos',3,4,[1,1.e-12]) displays the steps taken to compute

to 12 decimal places.

To find the minimum of the function

on the interval (0,2), write an M-file called f.m.

function y = f(x)
y = x.^3-2*x-5;

Then invoke fmin with

x = fmin('f', 0, 2)

The result is

x =
    0.8165

The value of the function at the minimum is

y = f(x)
          
y =
    -6.0887

Algorithm

The algorithm is based on golden section search and parabolic interpolation. A Fortran program implementing the same algorithms is given in [1].