fminbnd (MATLAB Function Reference)

Minimize a function of one variable

Syntax

x = fminbnd(fun,x1,x2)
x = fminbnd(fun,x1,x2,options)
x = fminbnd(fun,x1,x2,options,P1,P2,...)
[x,fval] = fminbnd(...)
[x,fval,exitflag] = fminbnd(...)
[x,fval,exitflag,output] = fminbnd(...)

Description

fminbnd finds the minimum of a function of one variable within a fixed interval.

x = fminbnd(fun,x1,x2)

returns a value x that is a local minimizer of the function that is described in fun (usually an M-file, built-in function, or inline object) in the interval x1 < x < x2. The function fun should return a scalar function value f when called with feval: f=feval(fun,x).

x = fminbnd(fun,x1,x2,options)

minimizes with the optimization parameters specified in the structure options. You can define these parameters using the optimset function. fminbnd uses these options structure fields:

Display - Level of display. off displays no output; iter displays output at each iteration; final displays just the final output.
MaxFunEvals - Maximum number of function evaluations allowed.
MaxIter - Maximum number of iterations allowed.
TolX - Termination tolerance on x.

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

provides for additional arguments, P1, P2, etc., which are passed to the objective function, fun(x,P1,P2,...). Use options=[] as a placeholder if no options are set.

[x,fval] = fminbnd(...)

returns the value of the objective function computed in fun at x.

[x,fval,exitflag] = fminbnd(...)

returns a value exitflag that describes the exit condition of fminbnd:

> 0 indicates that the function converged to a solution x.
0 indicates that the maximum number of function evaluations was reached.

[x,fval,exitflag,output] = fminbnd(...)

returns a structure output that contains information about the optimization:

output.algorithm - The algorithm used.
output.funcCount - The number of function evaluations.
output.iterations - The number of iterations taken.

Arguments

fun is a string containing the name of the function that computes the objective function to be minimized at the point x. The function returns one argument, a scalar valued function f to be minimized. For example, if fun='fun', the first line of the M-file fun.m is

f = fun(x)

fun can also be the name of a built-in function such as fun='sin'.

Alternatively, you can specify an inline object. For example,

fun = inline('sin(x*x)');

Other arguments are described in the syntax descriptions above.

Examples

x = fminbnd('cos',3,4) computes

to a few decimal places and gives a message on termination.

[x,fval,exitflag] =
   fminbnd('cos',3,4,optimset('TolX',1e-12,'Display','off'))

computes

to about 12 decimal places, suppresses output, returns the function value at x, and returns an exitflag of 1.

The argument fun can also be an inline function. To find the minimum of the function

on the interval (0,2), create an inline object f

f = inline('x.^3-2*x-5');

Then invoke fminbnd with

x = fminbnd(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 algorithm is given in [1].

Limitations

The function to be minimized must be continuous. fminbnd may only give local solutions.

fminbnd often exhibits slow convergence when the solution is on a boundary of the interval.

fminbnd only handles real variables.