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Minimize a function of one variable

Syntax

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:

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.

Then invoke fmin with

The result is

The value of the function at the minimum is

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       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.



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