CVX optimization for 2 dimensions variables

1

Dear All,
I have written my code :
`CVX `

n=10;
m=20;
L_tot=[1:1:10];

       cvx_begin
        variable f(n,m); % two dimensional matrix
        variable L(n,m); % two dimensional matrix
        dual variables A B C D E F
        minimize (sum(f.^2)+sum(power(2,2.*L/200)));
        subject to
        A: sum(L)-L_tot==0;
        B: -L<=0; 
        C: -R<=0;
        D: f-1000<= 0;
        E: L<=2*f ;
        F: 2*L-R<=0;
        cvx_end

but, Unfortunately, I am unable to solve the problem and this problem exist:

“Your objective function is not a scalar.”

but, the results seems scalar!!!

If possible, please help me how to resolve the problem.

Thanks all.

2

To the extent possible, CVX tries to adhere to the same conventions MATLAB does with its functions. For example, when X is a matrix, SUM(X) is a vector, not a scalar.

So that’s your problem here: quantities like sum(f.^2) are not scalars.

This is how I would write your objective: sum_square(vec(f))+sum(pow(2,2.*vec(L)/200))

Note that pow(2,x) is just exp(log(2)*x), which is subject to the standard warning about the use of exponentials, logarithms, etc. in CVX models.

3

I’ll only address the first term in the objective function, and leave the second term as an exercise for the OP.

f.^2 is an n by m matrix, hence sum(f.^2) is a 1 by m vector with the ith element being the sum of the ith column of f.^2. Hence it is not a scalar.

Your objective function needs to be scalar.

4

I checked: sum_square(vec(f))+sum(power(2,2.*vec(L)/200)), that is fine but, what is your opinion this solution for main aforementioned object to be: sum_square(f(:))+sum(power(2,2.*L(:)/200))?

5

That is fine too.