Absolute sum of non-diagonal elements

I have a minimization objective like this:

In my code I am trying to represent it as:

    variable X(size(A));
    idx = eye(size(A));
    Y = (1-idx).*X;
    minimize ( -log_det(X) + S * X + lambda * Y );

I am getting this error:

Your objective function is not a scalar.

A is a random matrix the same size as S.
Can you all please suggest what I am doing wrong? Thanks!

I suggest you read whatever paper or book you are getting this from more carefully and try to understand the material in it. Obviously, a non-scalar matrix objective function makes no sense, which would be apparent if you thought about it.

<S,X> means trace(S'*X), which is an affine function which can be directly entered into CVX. It also happens to equal sum(sum(S.*X)), which could be alternatively used.

S*X is a matrix, and therefore, per the rules of MATLAB, so is the objective function. Hence the CVX error ,message.

I don’t believe Y is correct. I believe
Y = trace((1-idx)*abs(X))
Y = sum(sum((1-idx).*abs(X))) would do the trick.

Actually it’s an assignment question.

I defined X as:

variable X(size(A));

Well, it’s better for you to understand your assignments, not blindly do things which don’t make any sense. Please ask your Prof to give me an A.