|MATLAB Function Reference|
Minimize a function of one variable on a fixed interval
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 in the interval
x1 <= x <= x2.
fun is a function handle. See Function Handles in the MATLAB Programming documentation for more information.
Parameterizing Functions Called by Function Functions, in the MATLAB mathematics documentation, explains how to provide additional parameters to the function
fun, if necessary.
x = fminbnd(fun,x1,x2,options)
minimizes with the optimization parameters specified in the structure
options. You can define these parameters using the
fminbnd uses these
options structure fields:
||Level of display.
||Check whether objective function values are valid.
||Maximum number of function evaluations allowed.
||Maximum number of iterations allowed.
||Specify a user-defined function that the optimization function calls at each iteration.
||Termination tolerance on
[x,fval] = fminbnd(...)
returns the value of the objective function computed in
[x,fval,exitflag] = fminbnd(...)
returns a value
exitflag that describes the exit condition of
||Maximum number of function evaluations or iterations was reached.
||Algorithm was terminated by the output function.
||Bounds are inconsistent (
[x,fval,exitflag,output] = fminbnd(...)
returns a structure
output that contains information about the optimization:
||Number of function evaluations
||Number of iterations
fun is the function to be minimized.
fun accepts a scalar
x and returns a scalar
f, the objective function evaluated at
x. The function
fun can be specified as a function handle for an M-file function
myfun.m is an M-file function such as
or as a function handle for an anonymous function:
Other arguments are described in the syntax descriptions above.
x = fminbnd(@cos,3,4) computes to a few decimal places and gives a message on termination.
computes to about 12 decimal places, suppresses output, returns the function value at
x, and returns an
exitflag of 1.
fun can also be a function handle for an anonymous function. For example, to find the minimum of the function on the interval
(0,2), create an anonymous function
The result is
The value of the function at the minimum is
fun is parameterized, you can use anonymous functions to capture the problem-dependent parameters. For example, suppose you want to minimize the objective function
myfun defined by the following M-file function.
myfun has an extra parameter
a, so you cannot pass it directly to
fminbind. To optimize for a specific value of
a, such as
a = 1.5.
fminbndwith a one-argument anonymous function that captures that value of
myfunwith two arguments:
fminbnd is an M-file. The algorithm is based on golden section search and parabolic interpolation. Unless the left endpoint x1 is very close to the right endpoint x2,
fminbnd never evaluates
fun at the endpoints, so
fun need only be defined for x in the interval x1 < x < x2. If the minimum actually occurs at x1 or x2,
fminbnd returns an interior point at a distance of no more than
2*TolX from x1 or x2, where
TolX is the termination tolerance. See  or  for details about the algorithm.
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.
@), anonymous functions
 Forsythe, G. E., M. A. Malcolm, and C. B. Moler, Computer Methods for Mathematical Computations, Prentice-Hall, 1976.
 Brent, Richard. P., Algorithms for Minimization without Derivatives, Prentice-Hall, Englewood Cliffs, New Jersey, 1973
© 1994-2005 The MathWorks, Inc.