To include a gradient in the objective function, have the objective return another output, as explained in the documentation.
You seem to have two definitions of your objective function in your script. The first one ( fun = @(x)…) looks good, in that you have just one variable x. Your second, function z = f(x,y)…, is not correct in that it takes two variables. See the link above for how to write scalar objective functions.
When you are done with your objective function it should look like this;
function [z,gz] = myfun(t)
x = t(1);
y = t(2);
z = (y - cos(2*x) - ((x.^2)/10)).^2 + exp((x.^2 + y.^2)/100);
if nargout > 1 % If a gradient is called for
gz(1) = 2*(y - cos(2*x) - ((x.^2)/10)).^2*(2*sin(2*x) - x/5)...
+ x/50*exp((x.^2 + y.^2)/100);
gz(2) = 2*(y - cos(2*x) - ((x.^2)/10)) + y/50*exp((x.^2 + y.^2)/100);
end
I hope that I didn't ruin your homework problem by giving you too explicit an answer.
Alan Weiss
MATLAB mathematical toolbox documentation
