MATLAB Mathematics - SERC - Index of

Minimizing Functions and Finding Zeros
Example of a Nested Output Function
The example in “Creating and Using an Output Function” on page 4-15 does
not require the output function to preserve data from one iteration to the next.
When this is the case, you can write the output function as an M-file and call
the optimization function directly from the command line. However, if you
want your output function to record data from one iteration to the next, you
should write a single M-file that does the following:
• Contains the output function as a nested function — see Nested Functions in
the online MATLAB documentation for more information.
• Calls the optimization function.
In the following example, the M-file also contains the objective function as a
subfunction, although you could also write the objective function as a separate
M-file or as an anonymous function.
Since the nested function has access to variables in the M-file function that
contains it, this method enables the output function to preserve variables from
one iteration to the next.
The following example uses an output function to record the points generated
by fminsearch in solving the optimization problem
minimize
x
fx ( ) e x 1 2 2
= ( 4x 1 + 2x 2 + 4x 1 x 2 + 2x 2 + 1)
and returns the sequence of points as a matrix called history.
To run the example, do the following steps:
1 Open a new M-file in the MATLAB editor.
2 Copy and paste the following code into the M-file.
function [x fval history] = myproblem(x0)
history = [];
options = optimset('OutputFcn', @myoutput);
[x fval] = fminsearch(@objfun, x0,options);
4-17