MATLAB Mathematics - SERC - Index of

Minimizing Functions and Finding Zeros
Stopping an Optimization Based on Data in optimValues. The output function can stop
an optimization at any iteration based on the current data in optimValues. For
example, the following code sets stop to true if the objective function value is
less than 5:
function stop = myoutput(x, optimValues, state)
stop = false;
% Check if objective function is less than 5.
if optimValues.fval < 5
stop = true;
end
Stopping an Optimization Based on GUI Input. If you design a GUI to perform
optimizations, you can make the output function stop an optimization when a
user clicks a Stop button on the GUI. The following code shows how to do this,
assuming that the Stop button callback stores the value true in the optimstop
field of a handles structure called hObject stored in appdata.
function stop = myoutput(x, optimValues, state)
stop = false;
% Check if user has requested to stop the optimization.
stop = getappdata(hObject,'optimstop');
Finding Zeros of Functions
The fzero function attempts to find a zero of one equation with one variable.
You can call this function with either a one-element starting point or a
two-element vector that designates a starting interval. If you give fzero a
starting point x0, fzero first searches for an interval around this point where
the function changes sign. If the interval is found, fzero returns a value near
where the function changes sign. If no such interval is found, fzero returns
NaN. Alternatively, if you know two points where the function value differs in
sign, you can specify this starting interval using a two-element vector; fzero is
guaranteed to narrow down the interval and return a value near a sign change.
The following sections contain two examples that illustrate how to find a zero
of a function using a starting interval and a starting point. The examples use
the function humps, which is provided with MATLAB. The following figure
shows the graph of humps.
4-21