Finding minimizers numerically in Matlab with 'fsolve' - matlab

Question

I'm completely new to Matlab and I've been having some problems with my code.
I need to use 'fsolve' to locate minimizers to a nonlinear optimization problem, but I can't get it to work.
I've been using the 'Solution Process of Nonlinear System' part from mathworks.
My code is the following:
function F = myfun(x)
F = [4*x(4) + 2*x(1) - x(3)*(2*x(1) + 4) + 4*x(1)*(x(1).^2 + x(2) - 11) + 2*x(2).^2 - 14;
x(3) - 10*x(4) + 2*x(2) + 4*x(2)*(x(2).^2 + x(1) - 7) + 2*x(1).^2 - 22;
x(2) - (x(1) + 2).^2;
4*x(1) - 10*x(2);];
x0 = [-5;-5];
options = optimoptions('fsolve','Display','iter');
[x,fval] = fsolve(#myfun,x0,options);
end
Where it says that; the value assigned to x appears to be unused as well as; not enough input arguments. But accoring to the mathworks page, I've done the exact same thing as them, so I'm sort of lost now.

Answer 1

There are several things that you are not doing correctly:
The function myfun must only contain equations (as mentioned in Florian's comment).
fsolve, x0 and options must be called from a separate script or from the Command Window.
The initial point array x0 must have at least as many elements as variables (x(4), x(3), x(2), x(1)) present in the equations in myfun.
Edit your function myfun, make sure that it only contains equations and save it in your working directory.
function F = myfun(x)
F = [4*x(4) + 2*x(1) - x(3)*(2*x(1) + 4) + 4*x(1)*(x(1)^2 + x(2) - 11) + 2*x(2)^2 - 14;
x(3) - 10*x(4) + 2*x(2) + 4*x(2)*(x(2)^2 + x(1) - 7) + 2*x(1)^2 - 22;
x(2) - (x(1) + 2)^2;
4*x(1) - 10*x(2)];
end
Note that you don't need to use the element-wise power operator .^. Using the ^ operator will be enough to define powers in your equations.
Now in the Command Window enter the following instructions:
x0 = [-5;-5;-5;-5];
options = optimoptions('fsolve','Display','iter');
[x,fval] = fsolve(#myfun,x0,options);
Note that I modified x0 to have at least 4 elements in order to match the number of equations that you defined in myfun. These are just sample values, so you should modify x0 with the values of your problem.
This is a fragment of the output:
Norm of First-order Trust-region
Iteration Func-count f(x) step optimality radius
0 5 81521 4.27e+04 1
1 10 12608.5 1 1.15e+04 1
2 15 966.243 2.5 1.71e+03 2.5
3 20 408.322 6.25 685 6.25
4 21 408.322 15.625 685 15.6
5 26 263.815 3.90625 244 3.91
6 27 263.815 9.76563 244 9.77
7 32 205.88 2.44141 272 2.44
8 37 138.11 6.10352 206 6.1
9 42 93.4561 6.10352 105 6.1
10 47 64.0129 6.10352 42.3 6.1
...