fmincon: proble defining the function

Hi, I am trying to solve a non linear constrained optimization. I report the few lines of code below:

%Here are the functions I use to define the objective function and the constraints

function Objective = definefunction(x)

comp1 = double(rand(180,3))
X = reshape(x,3,3);
comp2 = comp1*X;
comp3 = comp2(1:end, 3);
Objective = 0.5*comp3'*comp3/size(comp3,1);

end


function [c,ceq] = constraints(x)
Betas= rand(1,3)
c = [];
ceq(1) = x(1)^2 + x(4)^2 + x(7)^2;
ceq(2) = x(2)^2 + x(5)^2 + x(8)^2;
ceq(3) = x(3)^2 + x(6)^2 + x(9)^2;
ceq(4) = x(1)*x(2) + x(4)*x(5) + x(7)*x(8);
ceq(5) = x(1)*x(3) + x(4)*x(6) + x(7)*x(9);
ceq(6) = x(2)*x(3) + x(5)*x(6) + x(8)*x(9);
ceq(7) = x(4)*Betas(1,1) + x(5)*Betas(1,2) + x(6)*Betas(1,3);
ceq(8) = x(7)*Betas(1,1)  + x(8)*Betas(1,2)  + x(9)*Betas(1,3) ;
end

% define the objective function

f=definefunction(x);

% define constraints

nonlcon = @constraints;

% other inputs to the fmincon function

A = []; % No other constraints
b = [];
Aeq = [];
beq = [];
lb = [1., 1., 1., 0., 0., 0., 0., 0., .0];
ub = [1., 1., 1., 0., 0., 0., 0., .0, .0];
x0 = [0., 0., 0., 0., 0., 0., 0., .0, .0];

%implement

x = fmincon(f,x0,A,b,Aeq,beq,lb,ub,nonlcon)

Answer 1

[Torsten]

f = @definefunction;

instead of

f=definefunction(x);

And you cannot use random inputs on each call - thus

comp1 = double(rand(180,3))

and

Betas= rand(1,3)

within definefunction and nonlcon is not allowed because "fmincon" is a deterministic solver.

And the constraints

ceq(1) = x(1)^2 + x(4)^2 + x(7)^2;
ceq(2) = x(2)^2 + x(5)^2 + x(8)^2;
ceq(3) = x(3)^2 + x(6)^2 + x(9)^2;

immediately yield x(1) = x(2) = ... = x(9) = 0.

Maybe you could explain in your own words what problem you are trying to solve. It cannot be deduced from the code you provided.

[Walter Roberson]

Same with the betas in the constraints. The only routine that might work with stochastic systems is patternsearch (at least until you get into stochastic differential equations.)

[Vittoria Iannotta]

Thanks for the hints, I will try and come back. ok sorry for the rand(). I did it because in the routine I would have actual values coming from a regression, I did not want to overload the example. But you are right that written like this does not make sense.