fmin (MATLAB Function Reference)

Minimize a function of one variable

Note The fmin function was replaced by fminbnd in Release 11 (MATLAB 5.3). In Release 12 (MATLAB 6.0), fmin displays a warning message and calls 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.

`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].

See Also
fmins Minimize a function of several variables

fzero Find zero of a function of one variable

foptions in the Optimization Toolbox (or type help foptions).

References

[1] Forsythe, G. E., M. A. Malcolm, and C. B. Moler, Computer Methods for Mathematical Computations, Prentice-Hall, 1976.

flow fminbnd