Error from using rotated_lorentz: why is it concave?

I am a newbie to CVX, and am trying to build the following model:

    obj = 0;
    variable x(A, B);
    variable y(A, B);
    variable z(A, B);
    for i = 1:A
        for j =1:B
             obj = obj + x(i, j)
    subject to
    for i = 1:A
        for j = 1:B
            {x(i, j), y(i, j), C*log(1+C*z(i, j)) / log(2)} == rotated_lorentz(1);
....... (other constraints)

However, I get the error message: Disciplined convex programming error:
Invalid constraint: {concave} == {real affine}.
CVX does show that the constraint of my model is concave, but I have no idea why it is, since many posts seems to do similar things.

The error occurs because the 3rd argument on the left-hand side is nonlinear, rather than being affine as required.

Have you proven your model is convex?

Note that your objective can be more simply written as

Hi Mark,
Actually, the original constraint is sum(ylog(1 + z))>= C, where C is a constant, and I am aware that my formulation may not be convex due to the log and product term. I was trying this model because I see this approach from another paper, which introduces an auxiliary variable x and let sum(ylog(1+z))>=x^2 and x^2>=C, where the first one can be written as a rotated lorentz cone constraint: ||x||<=sqrt(sum(y*log(1+z))).

I appreciate your help and will try to find if there is anything wrong with my formulation.

Possibly try log(1+z)>=C*inv_pos(y).

Hi Michal,
Thank you for your suggestion! It works, but I found that my description is not elaborated.
C should be a constant for comparing the summation of y*log(1+z). I feel sorry :frowning:

I think you could show us the paper. What you write does not look convex.

Hi Michal,
Here is the paper:
This re-formulation is described at page 4 as equation (7a).


Unfortunately I cannot access it behind they paywall. Sorry.

Hi Machal,
Never mind. I came up with a solution by decomposing the original problem and solved them in an alternating fashion. The solution works. :slight_smile: Though I am still not sure if there is better approach to linearize this constraint, I defer this problem to the next stage. I really appreciate your help and suggestion.