fmincon problem, help needed

While running the code for optimization of a function, I run into the following error after the line:

x=fmincon(objective,x0,[],[],[],[],lb,ub,nonlincon);

Error using fmincon (line 619)

Supplied objective function must return a scalar value.

It is clear that the objective function is not scalar, but a vector. However I cannot find a solution.

Can anyone help?

The code is listed below.

var=importdata('Variables.txt'); % Import the variables [1,1…,low%,up%, low%, up%, …]

PQ=importdata('f.txt'); % Import i-th FEM frequency matrix, [j,i]: j-th variable, i-th mode

PM=importdata('fexp.txt'); % Import the vector of experimental frequencies {f1,f2,...,fm}

[v,m]=size(PQ); % extrapolation of number of variables (v-1)/2 and number of modes considered m

n=(v-1)/2;

C=ones(2*n+1); % generation of the unit coefficient matrix

for i= 2:2*n % loop to create the matrix containing the combination of the variables: base, low and up

if floor(i/2)*2==i % writing terms on the diagonal

C(:,i)=var(i/2);

C(:,i+1)=var(i/2).^2;

end

end

for i= 2:(2*n+1) % writing off-diagonal terms

if floor(i/2)*2==i

C(i,i)= var(n-1+i);

C(i,i+1)= var(n-1+i)^2;

C(i+1,i)= var(n+i);

C(i+1,i+1)= var(n+i)^2;

end

end

K=zeros(m,2*n+1); % matrix with the coefficients Ci,Ai,Bi

for i= 1:m

PQi=PQ(:,i);

K(i,:)=C\PQi; % calculation of the matrix with constants, (i,:) coefficients (Ci; Ai1; Bi1;... ;Aik; Bik)

% K(i,:) = C\PQi solves the system of linear equations C*K(i,:) = PQi

end

W= (1./PM); % diagonal matrix for normalized frequencies

objective = @(x)(sum(abs((PM-(K*x)).*W))); % objective function to be minimized

x0=ones(2*n+1,1); % Generation of the vector containing the variables

for i= 1:2*n

if floor(i/2)*2==i

x0(i)=var(i/2);

x0(i+1)=var(i/2).^2;

end

end

disp(x0);

disp(['initial Objective:' num2str(objective(x0))]);

disp(K*x0) % calculation of PQi

lb=ones(2*n+1,1); % definition of the lower bounds of the variables

ub=ones(2*n+1,1); % definition of the upper bounds of the variables

for i= 2:2*n

if floor(i/2)*2==i

ub(i,1)=var(n+(i),1);

ub(i+1,1)=var(n+(i),1).^2;

lb(i,1)=var(n-1+(i),1);

lb(i+1,1)=var(n-1+(i),1).^2;

end

end

nonlincon=@nlcon; % The nonlinear constraints defined in the function called "nlcon"

x=fmincon(objective,x0,[],[],[],[],lb,ub,nonlincon); % Application of the optimization algorithm

disp(['final Objective:' num2str(objective(x))]);

PQopt=K*x; % Calculation of optimized PQ parameters

erropt =(PQopt-PM)./PM % Percentage error between the PQopt and the experimental PMs

val_opt=x(2:2:end).*val_ini % Visualization of optimized variables

The function 'nlcon' is listed below:

function [c,ceq]=nlcon(x) % Function containing the nonlinear inequality and equality constraints

c = [];

for i= 2:(2*n) % Substitute the number of variables for n

if floor(i/2)*2==i

ceq(i/2,1)= x(i+1)-x(i).^2;

end

end

[Torsten]

It is clear that the objective function is not scalar, but a vector. However I cannot find a solution.

Can anyone help?

As long as you don't know which scalar value you want to minimize, we cannot help.

Maybe - since you deal with matrices - you have to sum twice to get the total sum of some matrix elements. But it's just a guess.

[medo_sk]

My objective function currently contains the following data:

>> objective(x0)

ans =

    1.3687    0.7673    0.9785
    

How do you propose to get scalar value?

I guess if I do 1.3687^2+0.7673^2+0.9785^2=3.42 would do the trick.

Is there any way to do this?

[Torsten]

If this is what you want:

objective = @(x)sum(sum(abs((PM-K*x).*W)).^2); % objective function to be minimized

[medo_sk]

Thank you.

This works!