Matrix input and matrix variables in minimization of an objective function

I have three variables S,V,B .Each variable is a 16*1 Matrix. I'd like to minimize an objective function, which is a summation of variables in these matrices. There are also some linear constraints for this model. I get the error "Not enough input arguments" on this optimization model:

    % [S,V,B,fval]=fmincon('objfun',x0,[],[],[],[],[-Inf(N,1),-Inf(N,1),zeros(N,1)],[Inf(N,1),Inf(N,1),ones(N,1)],'constraint');

I guess the way I define the input variables is not right.

I've attached the main code, the objective function and the constraints. I would be appreciated if you could take a look and help me.

Answer 1

[Titus Edelhofer]

Hi Hannaneh,

you need to have one vector of variables, not a matrix. So

• Your x0 should be ones(3*N,1), not ones(N,3)
• Your boundaries should be [-Inf(N,1); -Inf(N,1); zeros(N,1)], not [-Inf(N,1),-Inf(N,1),zeros(N,1)] (note the ";" instead of ",").
• Haven't looked into you objfun, but there you can change the x from (3*N)x1 back to Nx3 if it helps.

Titus

[Hannaneh]

Hello Titus,

Thank you so much for your reply. I made the changes you mentioned. I also changed the variables into an array:

% x=[S;V;B];
x0=ones(3*N,1);
[x,fval]=fmincon('objfun',x0,[],[],[],[],[-Inf(N,1);-Inf(N,1);zeros(N,1)],[Inf(N,1);Inf(N,1);ones(N,1)],'constraint');

However, I still get the same error. Maybe the problem is the objfun.m file itself.

Reagrds, Hannaneh

[Titus Edelhofer]

O.k., now I took a look at the objfun. And yes, the error states exactly the problem ;-). Your objfun should have exactly one input, but yours has two. I assume (!), that C, S, R in your objective function are the 3 variables (each with N entries)? In this case your objective function should be something like

function y = objfun(x)
C = x(1:N);
S = x(N + (1:N));
R = x(2*N + (1:N));
% do computation

Titus

[Hannaneh]

Thanks a lot!

I did this change both for the objective function and the constraints:

function f=objfun(x)
C = x(1:N);
S = x(N + (1:N));
R = x(2*N + (1:N));
% do computation
end

 function [c,ceq]=constraint(x)
 C = x(1:N);
 S = x(N + (1:N));
R = x(2*N + (1:N));
% constraints
end

No more "Not enough input arguments" error!Thank you! :) Although, the code is returning an answer, another error raised up:

_ * Error using fmincon User supplied objective function must return a scalar value. * _

Sorry for asking a lot, but it's strange that answer is not returned for variables?! Shall I ask this question in another converstation?

[Titus Edelhofer]

Again, the error tells you what's wrong ;-).

fmincon minimizes the value of the objective function. Therefore, the objfun should return a value, not a vector. Your function takes the sum, so it should be a scalar in fact.

My suggestion: put a breakpoint into your objfun (klick in the editor on one of the small lines next to the line number). A red bullet should appear. Run the code. Go stepwise through the code and see, what sizes the variables have, and esp. why at the end the return variable f is not a scalar ...

Titus